LMFDB - Embedded newform 225.2.p.b.68.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(32,225)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("225.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.p (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			68.3
Root			$0.430324 + 1.60599i$ of defining polynomial
Character	$\chi$	$=$	225.68
Dual form			225.2.p.b.182.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.430324 - 1.60599i) q^{2} +(-1.35314 + 1.08121i) q^{3} +(-0.661975 - 0.382191i) q^{4} +(1.15412 + 2.63840i) q^{6} +(1.73749 + 0.465559i) q^{7} +(1.45267 - 1.45267i) q^{8} +(0.661975 - 2.92605i) q^{9} +O(q^{10})$	\(q+(0.430324 - 1.60599i) q^{2} +(-1.35314 + 1.08121i) q^{3} +(-0.661975 - 0.382191i) q^{4} +(1.15412 + 2.63840i) q^{6} +(1.73749 + 0.465559i) q^{7} +(1.45267 - 1.45267i) q^{8} +(0.661975 - 2.92605i) q^{9} +(3.12636 - 1.80501i) q^{11} +(1.30897 - 0.198575i) q^{12} +(1.27850 - 0.342574i) q^{13} +(1.49537 - 2.59005i) q^{14} +(-2.47224 - 4.28205i) q^{16} +(-0.277007 - 0.277007i) q^{17} +(-4.41435 - 2.32228i) q^{18} +6.25273i q^{19} +(-2.85443 + 1.24862i) q^{21} +(-1.55348 - 5.79765i) q^{22} +(-0.579699 - 2.16347i) q^{23} +(-0.395027 + 3.53631i) q^{24} -2.20068i q^{26} +(2.26793 + 4.67509i) q^{27} +(-0.972242 - 0.972242i) q^{28} +(-1.56832 - 2.71642i) q^{29} +(-2.42605 + 4.20205i) q^{31} +(-3.97202 + 1.06430i) q^{32} +(-2.27882 + 5.82268i) q^{33} +(-0.564074 + 0.325668i) q^{34} +(-1.55652 + 1.68397i) q^{36} +(-5.55242 + 5.55242i) q^{37} +(10.0418 + 2.69070i) q^{38} +(-1.35960 + 1.84588i) q^{39} +(1.29036 + 0.744991i) q^{41} +(0.776946 + 5.12150i) q^{42} +(1.10121 - 4.10976i) q^{43} -2.75943 q^{44} -3.72396 q^{46} +(1.02368 - 3.82042i) q^{47} +(7.97508 + 3.12120i) q^{48} +(-3.26005 - 1.88219i) q^{49} +(0.674332 + 0.0753268i) q^{51} +(-0.977265 - 0.261857i) q^{52} +(-7.48222 + 7.48222i) q^{53} +(8.48410 - 1.63047i) q^{54} +(3.20031 - 1.84770i) q^{56} +(-6.76051 - 8.46082i) q^{57} +(-5.03742 + 1.34977i) q^{58} +(0.279377 - 0.483896i) q^{59} +(-2.96237 - 5.13097i) q^{61} +(5.70446 + 5.70446i) q^{62} +(2.51243 - 4.77580i) q^{63} -3.05196i q^{64} +(8.37054 + 6.16540i) q^{66} +(2.90325 + 10.8351i) q^{67} +(0.0775020 + 0.289242i) q^{68} +(3.12357 + 2.30070i) q^{69} +8.01611i q^{71} +(-3.28897 - 5.21223i) q^{72} +(1.29315 + 1.29315i) q^{73} +(6.52779 + 11.3065i) q^{74} +(2.38974 - 4.13915i) q^{76} +(6.27237 - 1.68068i) q^{77} +(2.37939 + 2.97783i) q^{78} +(6.96917 - 4.02365i) q^{79} +(-8.12358 - 3.87395i) q^{81} +(1.75172 - 1.75172i) q^{82} +(0.560714 + 0.150243i) q^{83} +(2.36678 + 0.264383i) q^{84} +(-6.12636 - 3.53706i) q^{86} +(5.05917 + 1.98001i) q^{87} +(1.91950 - 7.16367i) q^{88} -16.4343 q^{89} +2.38087 q^{91} +(-0.443112 + 1.65372i) q^{92} +(-1.26050 - 8.30903i) q^{93} +(-5.69504 - 3.28804i) q^{94} +(4.22396 - 5.73472i) q^{96} +(-5.14224 - 1.37786i) q^{97} +(-4.42566 + 4.42566i) q^{98} +(-3.21197 - 10.3428i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7}+O(q^{10}) $ 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7	$ 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7} + 6 q^{12} + 2 q^{13} - 8 q^{16} - 36 q^{18} - 12 q^{21} + 10 q^{22} - 18 q^{23} - 18 q^{27} + 16 q^{28} - 4 q^{31} - 30 q^{32} + 12 q^{33} - 48 q^{36} - 4 q^{37} + 30 q^{38} - 24 q^{41} - 6 q^{42} + 2 q^{43} + 32 q^{46} + 12 q^{47} + 30 q^{48} + 36 q^{51} + 14 q^{52} + 36 q^{56} + 6 q^{57} + 6 q^{58} + 8 q^{61} - 36 q^{63} + 36 q^{66} - 4 q^{67} - 42 q^{68} - 18 q^{72} + 8 q^{73} + 24 q^{76} + 6 q^{77} + 42 q^{78} - 48 q^{81} - 32 q^{82} + 66 q^{83} - 48 q^{86} + 18 q^{87} - 18 q^{88} - 40 q^{91} + 60 q^{92} + 18 q^{93} - 24 q^{96} - 28 q^{97}+O(q^{100}) $ 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7 + 6 * q^12 + 2 * q^13 - 8 * q^16 - 36 * q^18 - 12 * q^21 + 10 * q^22 - 18 * q^23 - 18 * q^27 + 16 * q^28 - 4 * q^31 - 30 * q^32 + 12 * q^33 - 48 * q^36 - 4 * q^37 + 30 * q^38 - 24 * q^41 - 6 * q^42 + 2 * q^43 + 32 * q^46 + 12 * q^47 + 30 * q^48 + 36 * q^51 + 14 * q^52 + 36 * q^56 + 6 * q^57 + 6 * q^58 + 8 * q^61 - 36 * q^63 + 36 * q^66 - 4 * q^67 - 42 * q^68 - 18 * q^72 + 8 * q^73 + 24 * q^76 + 6 * q^77 + 42 * q^78 - 48 * q^81 - 32 * q^82 + 66 * q^83 - 48 * q^86 + 18 * q^87 - 18 * q^88 - 40 * q^91 + 60 * q^92 + 18 * q^93 - 24 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.430324	−	1.60599i	0.304285	−	1.13561i	−0.629274	−	0.777183i	$-0.716648\pi$
$2$	0.430324	−	1.60599i	0.304285	−	1.13561i	0.933559	−	0.358423i	$-0.116686\pi$
$3$	−1.35314	+	1.08121i	−0.781236	+	0.624236i
$3$	−1.35314	+	1.08121i	−0.781236	+	0.624236i
$4$	−0.661975	−	0.382191i	−0.330987	−	0.191096i
$5$		0			0
$5$		0			0
$6$	1.15412	+	2.63840i	0.471169	+	1.07712i
$7$	1.73749	+	0.465559i	0.656710	+	0.175965i	0.571761	−	0.820421i	$-0.306261\pi$
$7$	1.73749	+	0.465559i	0.656710	+	0.175965i	0.0849489	+	0.996385i	$0.472927\pi$
$8$	1.45267	−	1.45267i	0.513598	−	0.513598i
$9$	0.661975	−	2.92605i	0.220658	−	0.975351i
$10$		0			0
$11$	3.12636	−	1.80501i	0.942634	−	0.544230i	0.0518493	−	0.998655i	$-0.483488\pi$
$11$	3.12636	−	1.80501i	0.942634	−	0.544230i	0.890785	+	0.454425i	$0.150155\pi$
$12$	1.30897	−	0.198575i	0.377868	−	0.0573236i
$13$	1.27850	−	0.342574i	0.354593	−	0.0950128i	−0.0771255	−	0.997021i	$-0.524574\pi$
$13$	1.27850	−	0.342574i	0.354593	−	0.0950128i	0.431718	+	0.902009i	$0.357908\pi$
$14$	1.49537	−	2.59005i	0.399654	−	0.692220i
$15$		0			0
$16$	−2.47224	−	4.28205i	−0.618061	−	1.07051i
$17$	−0.277007	−	0.277007i	−0.0671841	−	0.0671841i	0.672716	−	0.739900i	$-0.265127\pi$
$17$	−0.277007	−	0.277007i	−0.0671841	−	0.0671841i	−0.739900	+	0.672716i	$0.765127\pi$
$18$	−4.41435	−	2.32228i	−1.04047	−	0.547366i
$19$			6.25273i			1.43447i	0.696829	+	0.717237i	$0.254594\pi$
$19$			6.25273i			1.43447i	−0.696829	+	0.717237i	$0.745406\pi$
$20$		0			0
$21$	−2.85443	+	1.24862i	−0.622889	+	0.272472i
$22$	−1.55348	−	5.79765i	−0.331202	−	1.23606i
$23$	−0.579699	−	2.16347i	−0.120876	−	0.451114i	0.878784	−	0.477221i	$-0.158356\pi$
$23$	−0.579699	−	2.16347i	−0.120876	−	0.451114i	−0.999659	+	0.0261067i	$0.991689\pi$
$24$	−0.395027	+	3.53631i	−0.0806346	+	0.721847i
$25$		0			0
$26$		−	2.20068i		−	0.431589i
$27$	2.26793	+	4.67509i	0.436463	+	0.899722i
$28$	−0.972242	−	0.972242i	−0.183737	−	0.183737i
$29$	−1.56832	−	2.71642i	−0.291230	−	0.504426i	0.682871	−	0.730539i	$-0.260731\pi$
$29$	−1.56832	−	2.71642i	−0.291230	−	0.504426i	−0.974101	+	0.226114i	$0.927398\pi$
$30$		0			0
$31$	−2.42605	+	4.20205i	−0.435732	+	0.754710i	−0.997355	−	0.0726832i	$-0.976844\pi$
$31$	−2.42605	+	4.20205i	−0.435732	+	0.754710i	0.561623	+	0.827393i	$0.310177\pi$
$32$	−3.97202	+	1.06430i	−0.702160	+	0.188143i
$33$	−2.27882	+	5.82268i	−0.396691	+	1.01360i
$34$	−0.564074	+	0.325668i	−0.0967378	+	0.0558516i
$35$		0			0
$36$	−1.55652	+	1.68397i	−0.259421	+	0.280662i
$37$	−5.55242	+	5.55242i	−0.912812	+	0.912812i	−0.996493	−	0.0836807i	$-0.973332\pi$
$37$	−5.55242	+	5.55242i	−0.912812	+	0.912812i	0.0836807	+	0.996493i	$0.473332\pi$
$38$	10.0418	+	2.69070i	1.62900	+	0.436489i
$39$	−1.35960	+	1.84588i	−0.217710	+	0.295577i
$40$		0			0
$41$	1.29036	+	0.744991i	0.201521	+	0.116348i	0.597365	−	0.801970i	$-0.296215\pi$
$41$	1.29036	+	0.744991i	0.201521	+	0.116348i	−0.395844	+	0.918318i	$0.629548\pi$
$42$	0.776946	+	5.12150i	0.119885	+	0.790265i
$43$	1.10121	−	4.10976i	0.167933	−	0.626733i	−0.829715	−	0.558187i	$-0.811497\pi$
$43$	1.10121	−	4.10976i	0.167933	−	0.626733i	0.997648	−	0.0685463i	$-0.0218361\pi$
$44$	−2.75943			−0.416000
$45$		0			0
$46$	−3.72396			−0.549069
$47$	1.02368	−	3.82042i	0.149319	−	0.557266i	−0.850206	−	0.526450i	$-0.823523\pi$
$47$	1.02368	−	3.82042i	0.149319	−	0.557266i	0.999525	−	0.0308158i	$-0.00981053\pi$
$48$	7.97508	+	3.12120i	1.15110	+	0.450507i
$49$	−3.26005	−	1.88219i	−0.465722	−	0.268884i
$50$		0			0
$51$	0.674332	+	0.0753268i	0.0944254	+	0.0105479i
$52$	−0.977265	−	0.261857i	−0.135522	−	0.0363131i
$53$	−7.48222	+	7.48222i	−1.02776	+	1.02776i	−0.0281581	+	0.999603i	$0.508964\pi$
$53$	−7.48222	+	7.48222i	−1.02776	+	1.02776i	−0.999603	+	0.0281581i	$0.991036\pi$
$54$	8.48410	−	1.63047i	1.15454	−	0.221879i
$55$		0			0
$56$	3.20031	−	1.84770i	0.427660	−	0.246909i
$57$	−6.76051	−	8.46082i	−0.895451	−	1.12066i
$58$	−5.03742	+	1.34977i	−0.661446	+	0.177234i
$59$	0.279377	−	0.483896i	0.0363718	−	0.0629978i	−0.847266	−	0.531168i	$-0.821753\pi$
$59$	0.279377	−	0.483896i	0.0363718	−	0.0629978i	0.883638	+	0.468170i	$0.155087\pi$
$60$		0			0
$61$	−2.96237	−	5.13097i	−0.379292	−	0.656953i	0.611667	−	0.791115i	$-0.290499\pi$
$61$	−2.96237	−	5.13097i	−0.379292	−	0.656953i	−0.990959	+	0.134162i	$0.957166\pi$
$62$	5.70446	+	5.70446i	0.724467	+	0.724467i
$63$	2.51243	−	4.77580i	0.316536	−	0.601694i
$64$		−	3.05196i		−	0.381495i
$65$		0			0
$66$	8.37054	+	6.16540i	1.03034	+	0.758908i
$67$	2.90325	+	10.8351i	0.354688	+	1.32371i	0.880876	+	0.473346i	$0.156954\pi$
$67$	2.90325	+	10.8351i	0.354688	+	1.32371i	−0.526188	+	0.850368i	$0.676379\pi$
$68$	0.0775020	+	0.289242i	0.00939850	+	0.0350757i
$69$	3.12357	+	2.30070i	0.376034	+	0.276971i
$70$		0			0
$71$			8.01611i			0.951338i	0.879624	+	0.475669i	$0.157794\pi$
$71$			8.01611i			0.951338i	−0.879624	+	0.475669i	$0.842206\pi$
$72$	−3.28897	−	5.21223i	−0.387608	−	0.614268i
$73$	1.29315	+	1.29315i	0.151352	+	0.151352i	0.778721	−	0.627370i	$-0.215869\pi$
$73$	1.29315	+	1.29315i	0.151352	+	0.151352i	−0.627370	+	0.778721i	$0.715869\pi$
$74$	6.52779	+	11.3065i	0.758840	+	1.31435i
$75$		0			0
$76$	2.38974	−	4.13915i	0.274122	−	0.474793i
$77$	6.27237	−	1.68068i	0.714802	−	0.191531i
$78$	2.37939	+	2.97783i	0.269413	+	0.337172i
$79$	6.96917	−	4.02365i	0.784093	−	0.452696i	−0.0537859	−	0.998552i	$-0.517129\pi$
$79$	6.96917	−	4.02365i	0.784093	−	0.452696i	0.837879	+	0.545856i	$0.183796\pi$
$80$		0			0
$81$	−8.12358	−	3.87395i	−0.902620	−	0.430439i
$82$	1.75172	−	1.75172i	0.193445	−	0.193445i
$83$	0.560714	+	0.150243i	0.0615463	+	0.0164913i	0.289461	−	0.957190i	$-0.406524\pi$
$83$	0.560714	+	0.150243i	0.0615463	+	0.0164913i	−0.227914	+	0.973681i	$0.573191\pi$
$84$	2.36678	+	0.264383i	0.258237	+	0.0288465i
$85$		0			0
$86$	−6.12636	−	3.53706i	−0.660623	−	0.381411i
$87$	5.05917	+	1.98001i	0.542400	+	0.212279i
$88$	1.91950	−	7.16367i	0.204619	−	0.763650i
$89$	−16.4343			−1.74203			−0.871016	−	0.491255i	$-0.836538\pi$
$89$	−16.4343			−1.74203			−0.871016	+	0.491255i	$0.836538\pi$
$90$		0			0
$91$	2.38087			0.249583
$92$	−0.443112	+	1.65372i	−0.0461976	+	0.172412i
$93$	−1.26050	−	8.30903i	−0.130708	−	0.861606i
$94$	−5.69504	−	3.28804i	−0.587399	−	0.339135i
$95$		0			0
$96$	4.22396	−	5.73472i	0.431106	−	0.585298i
$97$	−5.14224	−	1.37786i	−0.522116	−	0.139900i	−0.0118706	−	0.999930i	$-0.503779\pi$
$97$	−5.14224	−	1.37786i	−0.522116	−	0.139900i	−0.510245	+	0.860029i	$0.670445\pi$
$98$	−4.42566	+	4.42566i	−0.447059	+	0.447059i
$99$	−3.21197	−	10.3428i	−0.322815	−	1.03949i
$100$		0			0
$101$	−4.73008	+	2.73092i	−0.470661	+	0.271736i	−0.716516	−	0.697570i	$-0.754265\pi$
$101$	−4.73008	+	2.73092i	−0.470661	+	0.271736i	0.245855	+	0.969307i	$0.420931\pi$
$102$	0.411155	−	1.05056i	0.0407104	−	0.104021i
$103$	−5.03410	+	1.34888i	−0.496024	+	0.132909i	−0.498154	−	0.867088i	$-0.665989\pi$
$103$	−5.03410	+	1.34888i	−0.496024	+	0.132909i	0.00212995	+	0.999998i	$0.499322\pi$
$104$	1.35960	−	2.35489i	0.133320	−	0.230916i
$105$		0			0
$106$	8.79659	+	15.2361i	0.854401	+	1.47987i
$107$	−4.07498	−	4.07498i	−0.393944	−	0.393944i	0.482147	−	0.876090i	$-0.339857\pi$
$107$	−4.07498	−	4.07498i	−0.393944	−	0.393944i	−0.876090	+	0.482147i	$0.839857\pi$
$108$	0.285467	−	3.96158i	0.0274691	−	0.381203i
$109$			1.10747i			0.106077i	0.998592	+	0.0530384i	$0.0168906\pi$
$109$			1.10747i			0.106077i	−0.998592	+	0.0530384i	$0.983109\pi$
$110$		0			0
$111$	1.50987	−	13.5165i	0.143311	−	1.28293i
$112$	−2.30195	−	8.59099i	−0.217514	−	0.811773i
$113$	−2.15985	−	8.06067i	−0.203182	−	0.758284i	−0.989996	−	0.141095i	$-0.954938\pi$
$113$	−2.15985	−	8.06067i	−0.203182	−	0.758284i	0.786815	−	0.617190i	$-0.211729\pi$
$114$	−16.4972	+	7.21642i	−1.54510	+	0.675879i
$115$		0			0
$116$			2.39760i			0.222611i
$117$	−0.156052	−	3.96774i	−0.0144270	−	0.366818i
$118$	−0.656909	−	0.656909i	−0.0604734	−	0.0604734i
$119$	−0.352334	−	0.610260i	−0.0322984	−	0.0559425i
$120$		0			0
$121$	1.01610	−	1.75994i	0.0923731	−	0.159995i
$122$	−9.51507	+	2.54955i	−0.861454	+	0.230826i
$123$	−2.55153	+	0.387074i	−0.230064	+	0.0349013i
$124$	3.21197	−	1.85443i	0.288444	−	0.166533i
$125$		0			0
$126$	−6.58873	−	6.09007i	−0.586971	−	0.542547i
$127$	11.5887	−	11.5887i	1.02833	−	1.02833i	0.0287470	−	0.999587i	$-0.490848\pi$
$127$	11.5887	−	11.5887i	1.02833	−	1.02833i	0.999587	−	0.0287470i	$-0.00915171\pi$
$128$	−12.8454	−	3.44193i	−1.13539	−	0.304226i
$129$	2.95342	+	6.75172i	0.260035	+	0.594456i
$130$		0			0
$131$	4.34401	+	2.50802i	0.379538	+	0.219126i	0.677617	−	0.735415i	$-0.263013\pi$
$131$	4.34401	+	2.50802i	0.379538	+	0.219126i	−0.298079	+	0.954541i	$0.596346\pi$
$132$	3.73390	−	2.98352i	0.324994	−	0.259682i
$133$	−2.91101	+	10.8641i	−0.252417	+	0.942033i
$134$	18.6504			1.61115
$135$		0			0
$136$	−0.804802			−0.0690112
$137$	0.118122	−	0.440837i	0.0100918	−	0.0376632i	−0.960696	−	0.277601i	$-0.910461\pi$
$137$	0.118122	−	0.440837i	0.0100918	−	0.0376632i	0.970788	+	0.239938i	$0.0771272\pi$
$138$	5.03904	−	4.02638i	0.428952	−	0.342748i
$139$	13.8860	+	8.01711i	1.17780	+	0.680003i	0.955504	−	0.294977i	$-0.0953120\pi$
$139$	13.8860	+	8.01711i	1.17780	+	0.680003i	0.222295	+	0.974980i	$0.428645\pi$
$140$		0			0
$141$	2.74549	+	6.27637i	0.231212	+	0.528566i
$142$	12.8738	+	3.44952i	1.08035	+	0.289478i
$143$	3.37872	−	3.37872i	0.282542	−	0.282542i
$144$	−14.1661	+	4.39930i	−1.18051	+	0.366609i
$145$		0			0
$146$	2.63326	−	1.52031i	0.217930	−	0.125822i
$147$	6.44635	−	0.977928i	0.531686	−	0.0806581i
$148$	5.79765	−	1.55348i	0.476564	−	0.127695i
$149$	3.44153	−	5.96090i	0.281941	−	0.488336i	−0.689922	−	0.723884i	$-0.742355\pi$
$149$	3.44153	−	5.96090i	0.281941	−	0.488336i	0.971863	+	0.235548i	$0.0756885\pi$
$150$		0			0
$151$	4.30647	+	7.45902i	0.350455	+	0.607006i	0.986329	−	0.164787i	$-0.0526935\pi$
$151$	4.30647	+	7.45902i	0.350455	+	0.607006i	−0.635874	+	0.771793i	$0.719360\pi$
$152$	9.08317	+	9.08317i	0.736743	+	0.736743i
$153$	−0.993910	+	0.627166i	−0.0803528	+	0.0507034i
$154$		−	10.7966i		−	0.870014i
$155$		0			0
$156$	1.60550	−	0.702298i	0.128543	−	0.0562288i
$157$	−0.431209	−	1.60930i	−0.0344142	−	0.128436i	0.946582	−	0.322464i	$-0.104511\pi$
$157$	−0.431209	−	1.60930i	−0.0344142	−	0.128436i	−0.980996	+	0.194029i	$0.937845\pi$
$158$	−3.46295	−	12.9239i	−0.275497	−	1.02817i
$159$	2.03465	−	18.2143i	0.161358	−	1.44449i
$160$		0			0
$161$		−	4.02889i		−	0.317521i
$162$	−9.71729	+	11.3793i	−0.763463	+	0.894045i
$163$	10.5120	+	10.5120i	0.823363	+	0.823363i	0.986589	−	0.163225i	$-0.0521898\pi$
$163$	10.5120	+	10.5120i	0.823363	+	0.823363i	−0.163225	+	0.986589i	$0.552190\pi$
$164$	−0.569458	−	0.986331i	−0.0444672	−	0.0770195i
$165$		0			0
$166$	0.482577	−	0.835848i	0.0374552	−	0.0648744i
$167$	−9.39195	+	2.51657i	−0.726771	+	0.194738i	−0.603191	−	0.797597i	$-0.706104\pi$
$167$	−9.39195	+	2.51657i	−0.726771	+	0.194738i	−0.123580	+	0.992335i	$0.539438\pi$
$168$	−2.33272	+	5.96040i	−0.179973	+	0.459855i
$169$	−9.74112	+	5.62404i	−0.749317	+	0.432618i
$170$		0			0
$171$	18.2958	+	4.13915i	1.39912	+	0.316529i
$172$	−2.29969	+	2.29969i	−0.175350	+	0.175350i
$173$	14.4929	+	3.88335i	1.10187	+	0.295246i	0.763527	−	0.645776i	$-0.223466\pi$
$173$	14.4929	+	3.88335i	1.10187	+	0.295246i	0.338346	+	0.941022i	$0.390133\pi$
$174$	5.35695	−	7.27294i	0.406109	−	0.551360i
$175$		0			0
$176$	−15.4583	−	8.92483i	−1.16521	−	0.672735i
$177$	0.145156	+	0.956844i	0.0109106	+	0.0719208i
$178$	−7.07207	+	26.3933i	−0.530074	+	1.97826i
$179$	4.21995			0.315414			0.157707	−	0.987486i	$-0.449590\pi$
$179$	4.21995			0.315414			0.157707	+	0.987486i	$0.449590\pi$
$180$		0			0
$181$	23.7930			1.76852			0.884261	−	0.466993i	$-0.154663\pi$
$181$	23.7930			1.76852			0.884261	+	0.466993i	$0.154663\pi$
$182$	1.02455	−	3.82366i	0.0759444	−	0.283428i
$183$	9.55615	+	3.73998i	0.706411	+	0.276468i
$184$	−3.98492	−	2.30070i	−0.293772	−	0.169610i
$185$		0			0
$186$	−13.8866	−	1.55122i	−1.01822	−	0.113741i
$187$	−1.36603	−	0.366025i	−0.0998937	−	0.0267664i
$188$	−2.13778	+	2.13778i	−0.155914	+	0.155914i
$189$	1.76397	+	9.17878i	0.128310	+	0.667658i
$190$		0			0
$191$	−20.1545	+	11.6362i	−1.45833	+	0.841965i	−0.998929	−	0.0462661i	$-0.985268\pi$
$191$	−20.1545	+	11.6362i	−1.45833	+	0.841965i	−0.459397	+	0.888231i	$0.651934\pi$
$192$	3.29980	+	4.12973i	0.238143	+	0.298037i
$193$	20.0285	−	5.36663i	1.44169	−	0.386299i	0.548562	−	0.836110i	$-0.315175\pi$
$193$	20.0285	−	5.36663i	1.44169	−	0.386299i	0.893124	+	0.449811i	$0.148509\pi$
$194$	−4.42566	+	7.66547i	−0.317744	+	0.550348i
$195$		0			0
$196$	1.43871	+	2.49193i	0.102765	+	0.177995i
$197$	−6.52613	−	6.52613i	−0.464968	−	0.464968i	0.435312	−	0.900280i	$-0.356638\pi$
$197$	−6.52613	−	6.52613i	−0.464968	−	0.464968i	−0.900280	+	0.435312i	$0.856638\pi$
$198$	−17.9926	+	0.707653i	−1.27868	+	0.0502907i
$199$		−	4.03778i		−	0.286231i	−0.989706	−	0.143115i	$-0.954288\pi$
$199$		−	4.03778i		−	0.286231i	0.989706	−	0.143115i	$-0.0457120\pi$
$200$		0			0
$201$	−15.6435	−	11.5223i	−1.10341	−	0.812724i
$202$	2.35036	+	8.77165i	0.165370	+	0.617171i
$203$	−1.46029	−	5.44989i	−0.102493	−	0.382507i
$204$	−0.417602	−	0.307588i	−0.0292380	−	0.0215355i
$205$		0			0
$206$			8.66517i			0.603731i
$207$	−6.71416	+	0.264070i	−0.466667	+	0.0183541i
$208$	−4.62768	−	4.62768i	−0.320872	−	0.320872i
$209$	11.2862	+	19.5483i	0.780684	+	1.35219i
$210$		0			0
$211$	0.653114	−	1.13123i	0.0449623	−	0.0778769i	−0.842668	−	0.538433i	$-0.819017\pi$
$211$	0.653114	−	1.13123i	0.0449623	−	0.0778769i	0.887631	+	0.460556i	$0.152350\pi$
$212$	7.81268	−	2.09340i	0.536577	−	0.143775i
$213$	−8.66709	−	10.8469i	−0.593859	−	0.743219i
$214$	−8.29795	+	4.79082i	−0.567236	+	0.327494i
$215$		0			0
$216$	10.0859	+	3.49682i	0.686262	+	0.237929i
$217$	−6.17155	+	6.17155i	−0.418952	+	0.418952i
$218$	1.77859	+	0.476572i	0.120461	+	0.0322776i
$219$	−3.14797	−	0.351647i	−0.212720	−	0.0237621i
$220$		0			0
$221$	−0.449050	−	0.259259i	−0.0302063	−	0.0174396i
$222$	−21.0577	−	8.24132i	−1.41330	−	0.553122i
$223$	2.14665	−	8.01142i	0.143751	−	0.536485i	−0.856057	−	0.516881i	$-0.827093\pi$
$223$	2.14665	−	8.01142i	0.143751	−	0.536485i	0.999808	−	0.0196035i	$-0.00624039\pi$
$224$	−7.39683			−0.494222
$225$		0			0
$226$	−13.8748			−0.922937
$227$	−2.38673	+	8.90739i	−0.158413	+	0.591204i	0.840376	+	0.542003i	$0.182334\pi$
$227$	−2.38673	+	8.90739i	−0.158413	+	0.591204i	−0.998789	+	0.0492007i	$0.984333\pi$
$228$	1.24163	+	8.18466i	0.0822292	+	0.542042i
$229$	17.2032	+	9.93228i	1.13682	+	0.656344i	0.945641	−	0.325211i	$-0.105435\pi$
$229$	17.2032	+	9.93228i	1.13682	+	0.656344i	0.191179	+	0.981555i	$0.438769\pi$
$230$		0			0
$231$	−6.67023	+	9.05593i	−0.438869	+	0.595836i
$232$	−6.22433	−	1.66780i	−0.408647	−	0.109497i
$233$	−5.45304	+	5.45304i	−0.357241	+	0.357241i	−0.862795	−	0.505554i	$-0.831288\pi$
$233$	−5.45304	+	5.45304i	−0.357241	+	0.357241i	0.505554	+	0.862795i	$0.331288\pi$
$234$	−6.43930	−	1.45679i	−0.420951	−	0.0952336i
$235$		0			0
$236$	−0.369882	+	0.213551i	−0.0240772	+	0.0139010i
$237$	−5.07985	+	12.9797i	−0.329972	+	0.843122i
$238$	−1.13169	+	0.303235i	−0.0733566	+	0.0196558i
$239$	−3.48185	+	6.03074i	−0.225222	+	0.390096i	−0.956386	−	0.292106i	$-0.905644\pi$
$239$	−3.48185	+	6.03074i	−0.225222	+	0.390096i	0.731164	+	0.682202i	$0.238977\pi$
$240$		0			0
$241$	−11.7660	−	20.3794i	−0.757918	−	1.31275i	−0.943911	−	0.330201i	$-0.892883\pi$
$241$	−11.7660	−	20.3794i	−0.757918	−	1.31275i	0.185993	−	0.982551i	$-0.440450\pi$
$242$	−2.38920	−	2.38920i	−0.153584	−	0.153584i
$243$	15.1809	−	3.54129i	0.973854	−	0.227174i
$244$			4.52877i			0.289925i
$245$		0			0
$246$	−0.476347	+	4.26430i	−0.0303708	+	0.271882i
$247$	2.14202	+	7.99413i	0.136293	+	0.508654i
$248$	2.57994	+	9.62847i	0.163826	+	0.611408i
$249$	−0.921168	+	0.402949i	−0.0583767	+	0.0255359i
$250$		0			0
$251$		−	20.7941i		−	1.31251i	−0.754537	−	0.656257i	$-0.772139\pi$
$251$		−	20.7941i		−	1.31251i	0.754537	−	0.656257i	$-0.227861\pi$
$252$	−3.48843	+	2.20123i	−0.219751	+	0.138665i
$253$	−5.71742	−	5.71742i	−0.359451	−	0.359451i
$254$	−13.6245	−	23.5983i	−0.854876	−	1.48069i
$255$		0			0
$256$	−8.00344	+	13.8624i	−0.500215	+	0.866398i
$257$	−10.1512	+	2.72001i	−0.633216	+	0.169670i	−0.561129	−	0.827729i	$-0.689633\pi$
$257$	−10.1512	+	2.72001i	−0.633216	+	0.169670i	−0.0720873	+	0.997398i	$0.522966\pi$
$258$	12.1141	−	1.83774i	0.754193	−	0.114413i
$259$	−12.2323	+	7.06229i	−0.760075	+	0.438830i
$260$		0			0
$261$	−8.98657	+	2.79080i	−0.556255	+	0.172746i
$262$	5.89718	−	5.89718i	0.364329	−	0.364329i
$263$	−14.4304	−	3.86662i	−0.889818	−	0.238426i	−0.215180	−	0.976574i	$-0.569034\pi$
$263$	−14.4304	−	3.86662i	−0.889818	−	0.238426i	−0.674638	+	0.738148i	$0.735700\pi$
$264$	5.14807	+	11.7688i	0.316842	+	0.724322i
$265$		0			0
$266$	16.1949	+	9.35012i	0.992972	+	0.573293i
$267$	22.2379	−	17.7689i	1.36094	−	1.08744i
$268$	2.21919	−	8.28214i	0.135559	−	0.505912i
$269$	−0.781994			−0.0476790			−0.0238395	−	0.999716i	$-0.507589\pi$
$269$	−0.781994			−0.0476790			−0.0238395	+	0.999716i	$0.507589\pi$
$270$		0			0
$271$	−12.4677			−0.757357			−0.378679	−	0.925528i	$-0.623621\pi$
$271$	−12.4677			−0.757357			−0.378679	+	0.925528i	$0.623621\pi$
$272$	−0.501329	+	1.87099i	−0.0303976	+	0.113445i
$273$	−3.22165	+	2.57422i	−0.194983	+	0.155799i
$274$	−0.657149	−	0.379405i	−0.0396998	−	0.0229207i
$275$		0			0
$276$	−1.18842	−	2.71681i	−0.0715345	−	0.163533i
$277$	−9.07336	−	2.43120i	−0.545165	−	0.146077i	−0.0242830	−	0.999705i	$-0.507730\pi$
$277$	−9.07336	−	2.43120i	−0.545165	−	0.146077i	−0.520882	+	0.853629i	$0.674397\pi$
$278$	18.8509	−	18.8509i	1.13060	−	1.13060i
$279$	10.6894	+	9.88041i	0.639959	+	0.591525i
$280$		0			0
$281$	26.6024	−	15.3589i	1.58697	−	0.916237i	0.593165	−	0.805081i	$-0.297878\pi$
$281$	26.6024	−	15.3589i	1.58697	−	0.916237i	0.993803	−	0.111156i	$-0.0354553\pi$
$282$	11.2612	−	1.70836i	0.670597	−	0.101731i
$283$	−18.1689	+	4.86835i	−1.08003	+	0.289393i	−0.754609	−	0.656175i	$-0.772173\pi$
$283$	−18.1689	+	4.86835i	−1.08003	+	0.289393i	−0.325423	+	0.945569i	$0.605507\pi$
$284$	3.06369	−	5.30647i	0.181797	−	0.314881i
$285$		0			0
$286$	−3.97224	−	6.88013i	−0.234884	−	0.406830i
$287$	1.89515	+	1.89515i	0.111867	+	0.111867i
$288$	0.484819	+	12.3269i	0.0285682	+	0.726368i
$289$		−	16.8465i		−	0.990973i
$290$		0			0
$291$	8.44793	−	3.69540i	0.495226	−	0.216628i
$292$	−0.361802	−	1.35026i	−0.0211728	−	0.0790181i
$293$	8.74817	+	32.6486i	0.511074	+	1.90735i	0.408880	+	0.912588i	$0.365919\pi$
$293$	8.74817	+	32.6486i	0.511074	+	1.90735i	0.102194	+	0.994765i	$0.467414\pi$
$294$	1.20347	−	10.7736i	0.0701880	−	0.628329i
$295$		0			0
$296$			16.1317i			0.937636i
$297$	15.5290	+	10.5224i	0.901081	+	0.610572i
$298$	−8.09218	−	8.09218i	−0.468767	−	0.468767i
$299$	−1.48229	−	2.56741i	−0.0857232	−	0.148477i
$300$		0			0
$301$	3.82668	−	6.62800i	0.220566	−	0.382031i
$302$	13.8323	−	3.70635i	0.795959	−	0.213276i
$303$	3.44778	−	8.80952i	0.198070	−	0.506094i
$304$	26.7745	−	15.4583i	1.53562	−	0.886592i
$305$		0			0
$306$	0.579519	+	1.86609i	0.0331289	+	0.106677i
$307$	2.26728	−	2.26728i	0.129400	−	0.129400i	−0.639440	−	0.768841i	$-0.720834\pi$
$307$	2.26728	−	2.26728i	0.129400	−	0.129400i	0.768841	+	0.639440i	$0.220834\pi$
$308$	−4.79449	−	1.28468i	−0.273191	−	0.0732014i
$309$	5.35341	−	7.26814i	0.304545	−	0.413470i
$310$		0			0
$311$	−1.86689	−	1.07785i	−0.105862	−	0.0611193i	0.446134	−	0.894966i	$-0.352800\pi$
$311$	−1.86689	−	1.07785i	−0.105862	−	0.0611193i	−0.551996	+	0.833847i	$0.686134\pi$
$312$	0.706405	+	4.65651i	0.0399923	+	0.263623i
$313$	5.62439	−	20.9905i	0.317909	−	1.18645i	−0.603341	−	0.797483i	$-0.706164\pi$
$313$	5.62439	−	20.9905i	0.317909	−	1.18645i	0.921250	−	0.388971i	$-0.127169\pi$
$314$	−2.77007			−0.156324
$315$		0			0
$316$	−6.15122			−0.346033
$317$	−1.20002	+	4.47853i	−0.0673997	+	0.251539i	−0.991403	−	0.130846i	$-0.958231\pi$
$317$	−1.20002	+	4.47853i	−0.0673997	+	0.251539i	0.924003	+	0.382385i	$0.124897\pi$
$318$	−28.3765	−	11.1057i	−1.59127	−	0.622776i
$319$	−9.80630	−	5.66167i	−0.549047	−	0.316993i
$320$		0			0
$321$	9.91993	+	1.10811i	0.553677	+	0.0618489i
$322$	−6.47035	−	1.73373i	−0.360579	−	0.0966167i
$323$	1.73205	−	1.73205i	0.0963739	−	0.0963739i
$324$	3.89702	+	5.66922i	0.216501	+	0.314957i
$325$		0			0
$326$	21.4057	−	12.3586i	1.18555	−	0.684480i
$327$	−1.19741	−	1.49857i	−0.0662170	−	0.0828709i
$328$	2.95670	−	0.792246i	0.163257	−	0.0437445i
$329$	3.55726	−	6.16136i	0.196118	−	0.339687i
$330$		0			0
$331$	14.5549	+	25.2097i	0.800007	+	1.38565i	0.919611	+	0.392831i	$0.128504\pi$
$331$	14.5549	+	25.2097i	0.800007	+	1.38565i	−0.119604	+	0.992822i	$0.538162\pi$
$332$	−0.313757	−	0.313757i	−0.0172197	−	0.0172197i
$333$	12.5711	+	19.9222i	0.688893	+	1.09173i
$334$			16.1663i			0.884582i
$335$		0			0
$336$	12.4035	+	9.13593i	0.676667	+	0.498406i
$337$	−6.47963	−	24.1823i	−0.352968	−	1.31729i	−0.883023	−	0.469330i	$-0.844495\pi$
$337$	−6.47963	−	24.1823i	−0.352968	−	1.31729i	0.530055	−	0.847963i	$-0.322171\pi$
$338$	4.84031	+	18.0643i	0.263278	+	0.982568i
$339$	11.6378	+	8.57197i	0.632081	+	0.465565i
$340$		0			0
$341$			17.5162i			0.948554i
$342$	14.5206	−	27.6017i	0.785182	−	1.49253i
$343$	−13.6916	−	13.6916i	−0.739274	−	0.739274i
$344$	−4.37045	−	7.56984i	−0.235639	−	0.408138i
$345$		0			0
$346$	12.4733	−	21.6043i	0.670566	−	1.16145i
$347$	33.7848	−	9.05260i	1.81366	−	0.485969i	0.817691	−	0.575657i	$-0.195254\pi$
$347$	33.7848	−	9.05260i	1.81366	−	0.485969i	0.995970	+	0.0896885i	$0.0285871\pi$
$348$	−2.59231	−	3.24429i	−0.138962	−	0.173912i
$349$	−17.0932	+	9.86876i	−0.914978	+	0.528263i	−0.882029	−	0.471194i	$-0.843823\pi$
$349$	−17.0932	+	9.86876i	−0.914978	+	0.528263i	−0.0329483	+	0.999457i	$0.510490\pi$
$350$		0			0
$351$	4.50112	+	5.20018i	0.240252	+	0.277565i
$352$	−10.4969	+	10.4969i	−0.559487	+	0.559487i
$353$	7.31017	+	1.95875i	0.389081	+	0.104254i	0.448056	−	0.894006i	$-0.352117\pi$
$353$	7.31017	+	1.95875i	0.389081	+	0.104254i	−0.0589749	+	0.998259i	$0.518783\pi$
$354$	1.59915	+	0.178634i	0.0849936	+	0.00949429i
$355$		0			0
$356$	10.8791	+	6.28105i	0.576591	+	0.332895i
$357$	1.13658	+	0.444821i	0.0601540	+	0.0235424i
$358$	1.81594	−	6.77720i	0.0959756	−	0.358186i
$359$	−8.47760			−0.447430			−0.223715	−	0.974655i	$-0.571819\pi$
$359$	−8.47760			−0.447430			−0.223715	+	0.974655i	$0.571819\pi$
$360$		0			0
$361$	−20.0966			−1.05772
$362$	10.2387	−	38.2114i	0.538135	−	2.00835i
$363$	0.527936	+	3.48007i	0.0277095	+	0.182656i
$364$	−1.57608	−	0.909949i	−0.0826089	−	0.0476943i
$365$		0			0
$366$	10.1186	−	13.7377i	0.528908	−	0.718080i
$367$	−7.93083	−	2.12506i	−0.413986	−	0.110927i	0.0458135	−	0.998950i	$-0.485412\pi$
$367$	−7.93083	−	2.12506i	−0.413986	−	0.110927i	−0.459799	+	0.888023i	$0.652079\pi$
$368$	−7.83091	+	7.83091i	−0.408215	+	0.408215i
$369$	3.03407	−	3.28250i	0.157947	−	0.170880i
$370$		0			0
$371$	−16.4837	+	9.51686i	−0.855791	+	0.494091i
$372$	−2.34122	+	5.98212i	−0.121387	+	0.310159i
$373$	−20.7853	+	5.56939i	−1.07622	+	0.288372i	−0.753046	−	0.657967i	$-0.771416\pi$
$373$	−20.7853	+	5.56939i	−1.07622	+	0.288372i	−0.323174	+	0.946340i	$0.604750\pi$
$374$	−1.17567	+	2.03631i	−0.0607923	+	0.105295i
$375$		0			0
$376$	−4.06275	−	7.03689i	−0.209520	−	0.362900i
$377$	−2.93568	−	2.93568i	−0.151195	−	0.151195i
$378$	15.5001	+	1.11692i	0.797240	+	0.0574483i
$379$		−	11.1614i		−	0.573325i	−0.958032	−	0.286663i	$-0.907454\pi$
$379$		−	11.1614i		−	0.573325i	0.958032	−	0.286663i	$-0.0925458\pi$
$380$		0			0
$381$	−3.15134	+	28.2110i	−0.161448	+	1.44529i
$382$	10.0147	+	37.3752i	0.512394	+	1.91228i
$383$	−3.93824	−	14.6977i	−0.201235	−	0.751018i	−0.990564	−	0.137049i	$-0.956238\pi$
$383$	−3.93824	−	14.6977i	−0.201235	−	0.751018i	0.789330	−	0.613970i	$-0.210428\pi$
$384$	21.1031	−	9.23120i	1.07691	−	0.471078i
$385$		0			0
$386$		−	34.4750i		−	1.75473i
$387$	−11.2964	−	5.94275i	−0.574229	−	0.302087i
$388$	2.87743	+	2.87743i	0.146079	+	0.146079i
$389$	−12.7395	−	22.0655i	−0.645920	−	1.11877i	−0.984088	−	0.177681i	$-0.943140\pi$
$389$	−12.7395	−	22.0655i	−0.645920	−	1.11877i	0.338168	−	0.941086i	$-0.390193\pi$
$390$		0			0
$391$	−0.438715	+	0.759876i	−0.0221868	+	0.0384286i
$392$	−7.47000	+	2.00158i	−0.377292	+	0.101095i
$393$	−8.58974	+	1.30309i	−0.433295	+	0.0657320i
$394$	−13.2893	+	7.67255i	−0.669503	+	0.386538i
$395$		0			0
$396$	−1.82668	+	8.07425i	−0.0917939	+	0.405746i
$397$	5.96779	−	5.96779i	0.299515	−	0.299515i	−0.541309	−	0.840824i	$-0.682071\pi$
$397$	5.96779	−	5.96779i	0.299515	−	0.299515i	0.840824	+	0.541309i	$0.182071\pi$
$398$	−6.48464	−	1.73755i	−0.325046	−	0.0870957i
$399$	−7.80730	−	17.8480i	−0.390854	−	0.893518i
$400$		0			0
$401$	23.6805	+	13.6719i	1.18255	+	0.682744i	0.956602	−	0.291396i	$-0.0941198\pi$
$401$	23.6805	+	13.6719i	1.18255	+	0.682744i	0.225945	+	0.974140i	$0.427453\pi$
$402$	−25.2365	+	20.1649i	−1.25868	+	1.00574i
$403$	−1.66220	+	6.20343i	−0.0828003	+	0.309015i
$404$	4.17493			0.207711
$405$		0			0
$406$	−9.38087			−0.465565
$407$	−7.33673	+	27.3810i	−0.363668	+	1.35723i
$408$	1.08901	−	0.870159i	0.0539140	−	0.0430793i
$409$	−23.5441	−	13.5932i	−1.16418	−	0.672140i	−0.211878	−	0.977296i	$-0.567958\pi$
$409$	−23.5441	−	13.5932i	−1.16418	−	0.672140i	−0.952302	+	0.305157i	$0.901291\pi$
$410$		0			0
$411$	0.316801	+	0.724228i	0.0156266	+	0.0357235i
$412$	3.84798	+	1.03106i	0.189576	+	0.0507968i
$413$	0.710697	−	0.710697i	0.0349711	−	0.0349711i
$414$	−2.46517	+	10.8965i	−0.121157	+	0.535535i
$415$		0			0
$416$	−4.71363	+	2.72142i	−0.231105	+	0.133428i
$417$	−27.4579	+	4.16544i	−1.34462	+	0.203983i
$418$	36.2511	−	9.71346i	1.77310	−	0.475101i
$419$	−15.7018	+	27.1964i	−0.767084	+	1.32863i	0.172053	+	0.985088i	$0.444960\pi$
$419$	−15.7018	+	27.1964i	−0.767084	+	1.32863i	−0.939138	+	0.343541i	$0.888373\pi$
$420$		0			0
$421$	−15.4328	−	26.7304i	−0.752150	−	1.30276i	−0.946779	−	0.321885i	$-0.895683\pi$
$421$	−15.4328	−	26.7304i	−0.752150	−	1.30276i	0.194629	−	0.980877i	$-0.437650\pi$
$422$	−1.53569	−	1.53569i	−0.0747562	−	0.0747562i
$423$	−10.5011	−	5.52436i	−0.510581	−	0.268604i
$424$			21.7384i			1.05571i
$425$		0			0
$426$	−21.1497	+	9.25158i	−1.02471	+	0.448240i
$427$	−2.75831	−	10.2942i	−0.133484	−	0.498170i
$428$	1.14011	+	4.25496i	0.0551095	+	0.205671i
$429$	−0.918778	+	8.22497i	−0.0443590	+	0.397105i
$430$		0			0
$431$		−	32.6869i		−	1.57447i	−0.616652	−	0.787236i	$-0.711511\pi$
$431$		−	32.6869i		−	1.57447i	0.616652	−	0.787236i	$-0.288489\pi$
$432$	14.4121	−	21.2694i	0.693403	−	1.02332i
$433$	7.25927	+	7.25927i	0.348858	+	0.348858i	0.859684	−	0.510826i	$-0.170660\pi$
$433$	7.25927	+	7.25927i	0.348858	+	0.348858i	−0.510826	+	0.859684i	$0.670660\pi$
$434$	7.25568	+	12.5672i	0.348284	+	0.603245i
$435$		0			0
$436$	0.423267	−	0.733120i	0.0202708	−	0.0351101i
$437$	13.5276	−	3.62470i	0.647111	−	0.173393i
$438$	−1.91939	+	4.90429i	−0.0917120	+	0.234336i
$439$	19.4684	−	11.2401i	0.929175	−	0.536459i	0.0426241	−	0.999091i	$-0.486428\pi$
$439$	19.4684	−	11.2401i	0.929175	−	0.536459i	0.886550	+	0.462632i	$0.153095\pi$
$440$		0			0
$441$	−7.66547	+	8.29312i	−0.365022	+	0.394911i
$442$	−0.609604	+	0.609604i	−0.0289959	+	0.0289959i
$443$	7.46524	+	2.00030i	0.354684	+	0.0950373i	0.431762	−	0.901988i	$-0.357892\pi$
$443$	7.46524	+	2.00030i	0.354684	+	0.0950373i	−0.0770774	+	0.997025i	$0.524559\pi$
$444$	−6.16540	+	8.37054i	−0.292597	+	0.397248i
$445$		0			0
$446$	−11.9425	−	6.89501i	−0.565494	−	0.326488i
$447$	1.78811	+	11.7869i	0.0845747	+	0.557503i
$448$	1.42087	−	5.30275i	0.0671297	−	0.250531i
$449$	38.1502			1.80042			0.900209	−	0.435458i	$-0.143414\pi$
$449$	38.1502			1.80042			0.900209	+	0.435458i	$0.143414\pi$
$450$		0			0
$451$	5.37886			0.253280
$452$	−1.65095	+	6.16144i	−0.0776543	+	0.289810i
$453$	−13.8920	−	5.43691i	−0.652703	−	0.255448i
$454$	13.2781	+	7.66612i	0.623173	+	0.359789i
$455$		0			0
$456$	−22.1116	−	2.47000i	−1.03547	−	0.115668i
$457$	26.9027	+	7.20855i	1.25845	+	0.337202i	0.825596	−	0.564261i	$-0.190839\pi$
$457$	26.9027	+	7.20855i	1.25845	+	0.337202i	0.432857	+	0.901463i	$0.357505\pi$
$458$	23.3541	−	23.3541i	1.09127	−	1.09127i
$459$	0.666801	−	1.92327i	0.0311236	−	0.0897704i
$460$		0			0
$461$	−21.2301	+	12.2572i	−0.988784	+	0.570874i	−0.904910	−	0.425602i	$-0.860062\pi$
$461$	−21.2301	+	12.2572i	−0.988784	+	0.570874i	−0.0838731	+	0.996476i	$0.526729\pi$
$462$	11.6734	+	14.6093i	0.543094	+	0.679686i
$463$	−17.2695	+	4.62735i	−0.802582	+	0.215051i	−0.636717	−	0.771097i	$-0.719708\pi$
$463$	−17.2695	+	4.62735i	−0.802582	+	0.215051i	−0.165865	+	0.986149i	$0.553042\pi$
$464$	−7.75455	+	13.4313i	−0.359996	+	0.623531i
$465$		0			0
$466$	6.41096	+	11.1041i	0.296982	+	0.514388i
$467$	−22.2894	−	22.2894i	−1.03143	−	1.03143i	−0.999490	−	0.0319412i	$-0.989831\pi$
$467$	−22.2894	−	22.2894i	−1.03143	−	1.03143i	−0.0319412	−	0.999490i	$-0.510169\pi$
$468$	−1.41313	+	2.68619i	−0.0653221	+	0.124169i
$469$			20.1775i			0.931709i
$470$		0			0
$471$	2.32347	+	1.71137i	0.107060	+	0.0788559i
$472$	−0.297098	−	1.10879i	−0.0136751	−	0.0510360i
$473$	−3.97538	−	14.8363i	−0.182788	−	0.682174i
$474$	18.6593	+	13.7437i	0.857049	+	0.631267i
$475$		0			0
$476$			0.538636i			0.0246883i
$477$	16.9403	+	26.8464i	0.775644	+	1.22921i
$478$	8.18699	+	8.18699i	0.374464	+	0.374464i
$479$	−6.76273	−	11.7134i	−0.308997	−	0.535199i	0.669146	−	0.743131i	$-0.266660\pi$
$479$	−6.76273	−	11.7134i	−0.308997	−	0.535199i	−0.978143	+	0.207932i	$0.933327\pi$
$480$		0			0
$481$	−5.19667	+	9.00089i	−0.236948	+	0.410405i
$482$	−37.7923	+	10.1264i	−1.72139	+	0.461246i
$483$	4.35607	+	5.45165i	0.198208	+	0.248058i
$484$	−1.34527	+	0.776693i	−0.0611487	+	0.0353042i
$485$		0			0
$486$	0.845418	−	25.9043i	0.0383489	−	1.17504i
$487$	−17.7890	+	17.7890i	−0.806094	+	0.806094i	−0.984040	−	0.177946i	$-0.943055\pi$
$487$	−17.7890	+	17.7890i	−0.806094	+	0.806094i	0.177946	+	0.984040i	$0.443055\pi$
$488$	−11.7570	−	3.15027i	−0.532213	−	0.142606i
$489$	−25.5899	−	2.85854i	−1.15721	−	0.129268i
$490$		0			0
$491$	−17.9785	−	10.3799i	−0.811359	−	0.468438i	0.0360688	−	0.999349i	$-0.488516\pi$
$491$	−17.9785	−	10.3799i	−0.811359	−	0.468438i	−0.847427	+	0.530911i	$0.821850\pi$
$492$	1.83699	+	0.718940i	0.0828177	+	0.0324123i
$493$	−0.318030	+	1.18690i	−0.0143233	+	0.0534554i
$494$	13.7603			0.619103
$495$		0			0
$496$	23.9912			1.07724
$497$	−3.73197	+	13.9279i	−0.167402	+	0.624752i
$498$	0.250732	+	1.65279i	0.0112356	+	0.0740631i
$499$	8.56156	+	4.94302i	0.383268	+	0.221280i	0.679239	−	0.733917i	$-0.262310\pi$
$499$	8.56156	+	4.94302i	0.383268	+	0.221280i	−0.295971	+	0.955197i	$0.595643\pi$
$500$		0			0
$501$	9.98769	−	13.5599i	0.446217	−	0.605813i
$502$	−33.3952	−	8.94821i	−1.49050	−	0.399378i
$503$	16.8084	−	16.8084i	0.749450	−	0.749450i	−0.224926	−	0.974376i	$-0.572214\pi$
$503$	16.8084	−	16.8084i	0.749450	−	0.749450i	0.974376	+	0.224926i	$0.0722140\pi$
$504$	−3.28794	−	10.5874i	−0.146457	−	0.471601i
$505$		0			0
$506$	−11.6425	+	6.72178i	−0.517571	+	0.298820i
$507$	7.10034	−	18.1423i	0.315337	−	0.805728i
$508$	−12.1006	+	3.24234i	−0.536876	+	0.143855i
$509$	20.1795	−	34.9520i	0.894442	−	1.54922i	0.0599475	−	0.998202i	$-0.480907\pi$
$509$	20.1795	−	34.9520i	0.894442	−	1.54922i	0.834494	−	0.551017i	$-0.185760\pi$
$510$		0			0
$511$	1.64480	+	2.84887i	0.0727615	+	0.126027i
$512$	0.0117190	+	0.0117190i	0.000517913	+	0.000517913i
$513$	−29.2321	+	14.1808i	−1.29063	+	0.626096i
$514$			17.4733i			0.770712i
$515$		0			0
$516$	0.625357	−	5.59824i	0.0275298	−	0.246449i
$517$	−3.69550	−	13.7918i	−0.162528	−	0.606562i
$518$	6.07815	+	22.6839i	0.267058	+	0.996675i
$519$	−23.8096	+	10.4151i	−1.04513	+	0.457172i
$520$		0			0
$521$			11.5144i			0.504456i	0.967668	+	0.252228i	$0.0811633\pi$
$521$			11.5144i			0.504456i	−0.967668	+	0.252228i	$0.918837\pi$
$522$	0.614861	+	15.6333i	0.0269118	+	0.684250i
$523$	29.5457	+	29.5457i	1.29194	+	1.29194i	0.933584	+	0.358358i	$0.116663\pi$
$523$	29.5457	+	29.5457i	1.29194	+	1.29194i	0.358358	+	0.933584i	$0.383337\pi$
$524$	−1.91708	−	3.32049i	−0.0837482	−	0.145056i
$525$		0			0
$526$	−12.4195	+	21.5112i	−0.541517	+	0.937934i
$527$	1.83603	−	0.491963i	0.0799788	−	0.0214303i
$528$	30.5668	−	4.63706i	1.33025	−	0.201802i
$529$	15.5740	−	8.99168i	0.677133	−	0.390943i
$530$		0			0
$531$	−1.23096	−	1.13780i	−0.0534193	−	0.0493763i
$532$	6.07917	−	6.07917i	0.263565	−	0.263565i
$533$	1.90494	+	0.510428i	0.0825123	+	0.0221091i
$534$	−18.9672	−	43.3602i	−0.820791	−	1.87638i
$535$		0			0
$536$	19.9573	+	11.5223i	0.862024	+	0.497690i
$537$	−5.71018	+	4.56265i	−0.246412	+	0.196893i
$538$	−0.336511	+	1.25587i	−0.0145080	+	0.0541446i
$539$	−13.5895			−0.585340
$540$		0			0
$541$	6.30670			0.271146			0.135573	−	0.990767i	$-0.456712\pi$
$541$	6.30670			0.271146			0.135573	+	0.990767i	$0.456712\pi$
$542$	−5.36514	+	20.0230i	−0.230452	+	0.860060i
$543$	−32.1953	+	25.7252i	−1.38163	+	1.10398i
$544$	1.39509	+	0.805458i	0.0598142	+	0.0345337i
$545$		0			0
$546$	2.74782	+	6.28169i	0.117596	+	0.268832i
$547$	29.8513	+	7.99863i	1.27635	+	0.341997i	0.832460	−	0.554085i	$-0.186932\pi$
$547$	29.8513	+	7.99863i	1.27635	+	0.341997i	0.443889	+	0.896082i	$0.353599\pi$
$548$	−0.246678	+	0.246678i	−0.0105375	+	0.0105375i
$549$	−16.9745	+	5.27147i	−0.724454	+	0.224981i
$550$		0			0
$551$	16.9850	−	9.80630i	0.723586	−	0.417762i
$552$	7.87969	−	1.19537i	0.335382	−	0.0508783i
$553$	13.9821	−	3.74650i	0.594580	−	0.159317i
$554$	−7.80896	+	13.5255i	−0.331771	+	0.574644i
$555$		0			0
$556$	−6.12814	−	10.6143i	−0.259891	−	0.450145i
$557$	6.63181	+	6.63181i	0.280999	+	0.280999i	0.833507	−	0.552509i	$-0.186329\pi$
$557$	6.63181	+	6.63181i	0.280999	+	0.280999i	−0.552509	+	0.833507i	$0.686329\pi$
$558$	20.4678	−	12.9153i	0.866469	−	0.546750i
$559$		−	5.63159i		−	0.238191i
$560$		0			0
$561$	2.24417	−	0.981675i	0.0947491	−	0.0414464i
$562$	−13.2186	−	49.3326i	−0.557594	−	2.08097i
$563$	4.87751	+	18.2031i	0.205563	+	0.767170i	0.989277	+	0.146049i	$0.0466558\pi$
$563$	4.87751	+	18.2031i	0.205563	+	0.767170i	−0.783715	+	0.621121i	$0.786678\pi$
$564$	0.581329	−	5.20411i	0.0244784	−	0.219132i
$565$		0			0
$566$			31.2741i			1.31455i
$567$	−12.3111	−	10.5130i	−0.517017	−	0.441503i
$568$	11.6448	+	11.6448i	0.488605	+	0.488605i
$569$	10.4878	+	18.1654i	0.439670	+	0.761531i	0.997664	−	0.0683141i	$-0.0217620\pi$
$569$	10.4878	+	18.1654i	0.439670	+	0.761531i	−0.557994	+	0.829845i	$0.688429\pi$
$570$		0			0
$571$	−12.2406	+	21.2014i	−0.512254	+	0.887250i	0.487645	+	0.873042i	$0.337856\pi$
$571$	−12.2406	+	21.2014i	−0.512254	+	0.887250i	−0.999899	+	0.0142078i	$0.995477\pi$
$572$	−3.52794	+	0.945309i	−0.147511	+	0.0395254i
$573$	14.6907	−	37.5366i	0.613711	−	1.56811i
$574$	3.85913	−	2.22807i	0.161077	−	0.0929978i
$575$		0			0
$576$	−8.93019	−	2.02032i	−0.372091	−	0.0841800i
$577$	12.4198	−	12.4198i	0.517041	−	0.517041i	−0.399634	−	0.916675i	$-0.630863\pi$
$577$	12.4198	−	12.4198i	0.517041	−	0.517041i	0.916675	+	0.399634i	$0.130863\pi$
$578$	−27.0554	−	7.24946i	−1.12535	−	0.301538i
$579$	−21.2990	+	28.9168i	−0.885155	+	1.20174i
$580$		0			0
$581$	0.904288	+	0.522091i	0.0375162	+	0.0216600i
$582$	−2.29943	−	15.1575i	−0.0953146	−	0.628299i
$583$	−9.88668	+	36.8976i	−0.409465	+	1.52814i
$584$	3.75705			0.155468
$585$		0			0
$586$	56.1979			2.32151
$587$	−3.91669	+	14.6173i	−0.161659	+	0.603320i	0.836784	+	0.547534i	$0.184433\pi$
$587$	−3.91669	+	14.6173i	−0.161659	+	0.603320i	−0.998443	+	0.0557861i	$0.982234\pi$
$588$	−4.64108	−	1.81637i	−0.191395	−	0.0749060i
$589$	−26.2743	−	15.1695i	−1.08261	−	0.625047i
$590$		0			0
$591$	15.8869	+	1.77466i	0.653499	+	0.0729997i
$592$	37.5027	+	10.0488i	1.54135	+	0.413003i
$593$	−12.8270	+	12.8270i	−0.526744	+	0.526744i	−0.919600	−	0.392856i	$-0.871487\pi$
$593$	−12.8270	+	12.8270i	−0.526744	+	0.526744i	0.392856	+	0.919600i	$0.371487\pi$
$594$	23.5814	−	20.4113i	0.967555	−	0.837486i
$595$		0			0
$596$	−4.55641	+	2.63064i	−0.186638	+	0.107755i
$597$	4.36569	+	5.46368i	0.178676	+	0.223614i
$598$	−4.76109	+	1.27573i	−0.194696	+	0.0521685i
$599$	3.45057	−	5.97656i	0.140987	−	0.244196i	−0.786882	−	0.617104i	$-0.788306\pi$
$599$	3.45057	−	5.97656i	0.140987	−	0.244196i	0.927868	+	0.372908i	$0.121639\pi$
$600$		0			0
$601$	6.29969	+	10.9114i	0.256970	+	0.445085i	0.965429	−	0.260667i	$-0.0839426\pi$
$601$	6.29969	+	10.9114i	0.256970	+	0.445085i	−0.708459	+	0.705752i	$0.750609\pi$
$602$	−8.99779	−	8.99779i	−0.366722	−	0.366722i
$603$	33.6259	−	1.32251i	1.36935	−	0.0538570i
$604$		−	6.58358i		−	0.267882i
$605$		0			0
$606$	−12.6643	−	9.32804i	−0.514454	−	0.378926i
$607$	9.63152	+	35.9453i	0.390931	+	1.45898i	0.828601	+	0.559839i	$0.189137\pi$
$607$	9.63152	+	35.9453i	0.390931	+	1.45898i	−0.437670	+	0.899136i	$0.644196\pi$
$608$	−6.65477	−	24.8359i	−0.269887	−	1.00723i
$609$	7.86845	+	5.79558i	0.318846	+	0.234849i
$610$		0			0
$611$		−	5.23510i		−	0.211789i
$612$	0.897641	−	0.0353045i	0.0362850	−	0.00142710i
$613$	−12.4072	−	12.4072i	−0.501121	−	0.501121i	0.410665	−	0.911786i	$-0.365296\pi$
$613$	−12.4072	−	12.4072i	−0.501121	−	0.501121i	−0.911786	+	0.410665i	$0.865296\pi$
$614$	−2.66556	−	4.61689i	−0.107573	−	0.186322i
$615$		0			0
$616$	6.67023	−	11.5532i	0.268751	−	0.465491i
$617$	9.92141	−	2.65843i	0.399421	−	0.107025i	−0.0535162	−	0.998567i	$-0.517043\pi$
$617$	9.92141	−	2.65843i	0.399421	−	0.107025i	0.452937	+	0.891542i	$0.350376\pi$
$618$	−9.36885	−	11.7252i	−0.376871	−	0.471656i
$619$	19.1639	−	11.0643i	0.770264	−	0.444712i	−0.0627048	−	0.998032i	$-0.519973\pi$
$619$	19.1639	−	11.0643i	0.770264	−	0.444712i	0.832969	+	0.553320i	$0.186639\pi$
$620$		0			0
$621$	8.79969	−	7.61674i	0.353119	−	0.305649i
$622$	−2.53439	+	2.53439i	−0.101620	+	0.101620i
$623$	−28.5544	−	7.65114i	−1.14401	−	0.306536i
$624$	11.2654	+	1.25841i	0.450977	+	0.0503767i
$625$		0			0
$626$	−31.2902	−	18.0654i	−1.25061	−	0.722040i
$627$	−36.4076	−	14.2488i	−1.45398	−	0.569044i
$628$	−0.329609	+	1.23012i	−0.0131528	+	0.0490870i
$629$	3.07612			0.122653
$630$		0			0
$631$	8.15013			0.324451			0.162226	−	0.986754i	$-0.448133\pi$
$631$	8.15013			0.324451			0.162226	+	0.986754i	$0.448133\pi$
$632$	4.27888	−	15.9690i	0.170205	−	0.635212i
$633$	0.339338	+	2.23686i	0.0134875	+	0.0889073i
$634$	6.67608	+	3.85443i	0.265141	+	0.153079i
$635$		0			0
$636$	−8.30824	+	11.2798i	−0.329443	+	0.447273i
$637$	−4.81277	−	1.28958i	−0.190689	−	0.0510949i
$638$	−13.3125	+	13.3125i	−0.527046	+	0.527046i
$639$	23.4556	+	5.30647i	0.927888	+	0.209921i
$640$		0			0
$641$	−2.49058	+	1.43794i	−0.0983722	+	0.0567952i	−0.548379	−	0.836230i	$-0.684755\pi$
$641$	−2.49058	+	1.43794i	−0.0983722	+	0.0567952i	0.450007	+	0.893025i	$0.351422\pi$
$642$	6.04840	−	15.4545i	0.238711	−	0.609939i
$643$	9.50279	−	2.54626i	0.374753	−	0.100415i	−0.0665259	−	0.997785i	$-0.521191\pi$
$643$	9.50279	−	2.54626i	0.374753	−	0.100415i	0.441279	+	0.897370i	$0.354525\pi$
$644$	−1.53981	+	2.66702i	−0.0606768	+	0.105095i
$645$		0			0
$646$	−2.03631	−	3.52700i	−0.0801177	−	0.138768i
$647$	14.2662	+	14.2662i	0.560862	+	0.560862i	0.929552	−	0.368691i	$-0.120194\pi$
$647$	14.2662	+	14.2662i	0.560862	+	0.560862i	−0.368691	+	0.929552i	$0.620194\pi$
$648$	−17.4285	+	6.17332i	−0.684656	+	0.242511i
$649$		−	2.01711i		−	0.0791786i
$650$		0			0
$651$	1.67823	−	15.0237i	0.0657752	−	0.588825i
$652$	−2.94108	−	10.9763i	−0.115182	−	0.429864i
$653$	−10.2780	−	38.3580i	−0.402209	−	1.50106i	−0.809146	−	0.587607i	$-0.800070\pi$
$653$	−10.2780	−	38.3580i	−0.402209	−	1.50106i	0.406937	−	0.913456i	$-0.366597\pi$
$654$	−2.92196	+	1.27816i	−0.114258	+	0.0499800i
$655$		0			0
$656$		−	7.36719i		−	0.287641i
$657$	4.63985	−	2.92779i	0.181018	−	0.114224i
$658$	−8.36431	−	8.36431i	−0.326075	−	0.326075i
$659$	23.3689	+	40.4762i	0.910324	+	1.57673i	0.813607	+	0.581415i	$0.197501\pi$
$659$	23.3689	+	40.4762i	0.910324	+	1.57673i	0.0967171	+	0.995312i	$0.469166\pi$
$660$		0			0
$661$	−2.81433	+	4.87455i	−0.109465	+	0.189598i	−0.915553	−	0.402196i	$-0.868247\pi$
$661$	−2.81433	+	4.87455i	−0.109465	+	0.189598i	0.806089	+	0.591794i	$0.201580\pi$
$662$	46.7499	−	12.5266i	1.81699	−	0.486860i
$663$	0.887940	−	0.134703i	0.0344847	−	0.00523142i
$664$	1.03279	−	0.596280i	0.0400799	−	0.0231402i
$665$		0			0
$666$	37.4046	−	11.6161i	1.44940	−	0.450114i
$667$	−4.96772	+	4.96772i	−0.192351	+	0.192351i
$668$	7.17905	+	1.92362i	0.277766	+	0.0744271i
$669$	5.75730	+	13.1616i	0.222590	+	0.508855i
$670$		0			0
$671$	−18.5229	−	10.6942i	−0.715068	−	0.412845i
$672$	10.0089	−	7.99752i	0.386104	−	0.308511i
$673$	7.71528	−	28.7938i	0.297402	−	1.10992i	−0.641888	−	0.766798i	$-0.721849\pi$
$673$	7.71528	−	28.7938i	0.297402	−	1.10992i	0.939291	−	0.343122i	$-0.111485\pi$
$674$	−41.6249			−1.60333
$675$		0			0
$676$	8.59784			0.330686
$677$	12.9376	−	48.2839i	0.497234	−	1.85570i	−0.0199076	−	0.999802i	$-0.506337\pi$
$677$	12.9376	−	48.2839i	0.497234	−	1.85570i	0.517141	−	0.855900i	$-0.326996\pi$
$678$	18.7745	−	15.0015i	0.721032	−	0.576131i
$679$	−8.29312	−	4.78804i	−0.318261	−	0.183748i
$680$		0			0
$681$	−6.40117	−	14.6335i	−0.245293	−	0.560757i
$682$	28.1308	+	7.53763i	1.07718	+	0.288631i
$683$	4.38271	−	4.38271i	0.167700	−	0.167700i	−0.618268	−	0.785968i	$-0.712165\pi$
$683$	4.38271	−	4.38271i	0.167700	−	0.167700i	0.785968	+	0.618268i	$0.212165\pi$
$684$	−10.5294	−	9.73252i	−0.402603	−	0.372132i
$685$		0			0
$686$	−27.8803	+	16.0967i	−1.06447	+	0.614575i
$687$	−34.0172	+	5.16050i	−1.29784	+	0.196886i
$688$	−20.3207	+	5.44491i	−0.774718	+	0.207585i
$689$	−7.00282	+	12.1292i	−0.266786	+	0.462087i
$690$		0			0
$691$	−0.346648	−	0.600412i	−0.0131871	−	0.0228407i	0.859357	−	0.511377i	$-0.170864\pi$
$691$	−0.346648	−	0.600412i	−0.0131871	−	0.0228407i	−0.872544	+	0.488536i	$0.837531\pi$
$692$	−8.10973	−	8.10973i	−0.308286	−	0.308286i
$693$	−0.765597	−	19.4658i	−0.0290826	−	0.739446i
$694$		−	58.1535i		−	2.20748i
$695$		0			0
$696$	10.2256	−	4.47303i	0.387601	−	0.169550i
$697$	−0.151072	−	0.563807i	−0.00572225	−	0.0213557i
$698$	8.49352	+	31.6983i	0.321485	+	1.19980i
$699$	1.48285	−	13.2746i	0.0560866	−	0.502092i
$700$		0			0
$701$			8.36037i			0.315767i	0.987458	+	0.157883i	$0.0504670\pi$
$701$			8.36037i			0.315767i	−0.987458	+	0.157883i	$0.949533\pi$
$702$	10.2884	−	4.99099i	0.388310	−	0.188373i
$703$	−34.7178	−	34.7178i	−1.30941	−	1.30941i
$704$	−5.50881	−	9.54154i	−0.207621	−	0.359610i
$705$		0			0
$706$	6.29148	−	10.8972i	0.236783	−	0.410120i
$707$	−9.48988	+	2.54281i	−0.356904	+	0.0956320i
$708$	0.269608	−	0.688884i	0.0101325	−	0.0258898i
$709$	−4.59399	+	2.65234i	−0.172531	+	0.0996109i	−0.583779	−	0.811913i	$-0.698426\pi$
$709$	−4.59399	+	2.65234i	−0.172531	+	0.0996109i	0.411248	+	0.911524i	$0.365093\pi$
$710$		0			0
$711$	−7.16001	−	23.0557i	−0.268521	−	0.864657i
$712$	−23.8737	+	23.8737i	−0.894704	+	0.894704i
$713$	10.4974	+	2.81276i	0.393130	+	0.105339i
$714$	1.20347	−	1.63391i	0.0450389	−	0.0611477i
$715$		0			0
$716$	−2.79350	−	1.61283i	−0.104398	−	0.0602742i
$717$	−1.80906	−	11.9250i	−0.0675606	−	0.445349i
$718$	−3.64811	+	13.6149i	−0.136146	+	0.508105i
$719$	28.3121			1.05586			0.527932	−	0.849286i	$-0.322967\pi$
$719$	28.3121			1.05586			0.527932	+	0.849286i	$0.322967\pi$
$720$		0			0
$721$	−9.37468			−0.349131
$722$	−8.64806	+	32.2750i	−0.321847	+	1.20115i
$723$	37.9555	+	14.8546i	1.41158	+	0.552449i
$724$	−15.7504	−	9.09349i	−0.585359	−	0.337957i
$725$		0			0
$726$	5.81614	+	0.649697i	0.215857	+	0.0241125i
$727$	−43.4720	−	11.6483i	−1.61229	−	0.432011i	−0.663565	−	0.748119i	$-0.730957\pi$
$727$	−43.4720	−	11.6483i	−1.61229	−	0.432011i	−0.948723	+	0.316108i	$0.897624\pi$
$728$	3.45863	−	3.45863i	0.128185	−	0.128185i
$729$	−16.7130	+	21.2056i	−0.618999	+	0.785391i
$730$		0			0
$731$	−1.44348	+	0.833392i	−0.0533889	+	0.0308241i
$732$	−4.89654	−	6.12805i	−0.180981	−	0.226499i
$733$	23.3565	−	6.25836i	0.862693	−	0.231158i	0.199768	−	0.979843i	$-0.435981\pi$
$733$	23.3565	−	6.25836i	0.862693	−	0.231158i	0.662926	+	0.748685i	$0.269315\pi$
$734$	−6.82565	+	11.8224i	−0.251939	+	0.436372i
$735$		0			0
$736$	4.60515	+	7.97635i	0.169748	+	0.294012i
$737$	28.6340	+	28.6340i	1.05475	+	1.05475i
$738$	−3.96604	−	6.28523i	−0.145992	−	0.231362i
$739$		−	5.60736i		−	0.206270i	−0.994667	−	0.103135i	$-0.967113\pi$
$739$		−	5.60736i		−	0.206270i	0.994667	−	0.103135i	$-0.0328874\pi$
$740$		0			0
$741$	−11.5418	−	8.50120i	−0.423998	−	0.312299i
$742$	8.19067	+	30.5680i	0.300689	+	1.12219i
$743$	2.21018	+	8.24852i	0.0810838	+	0.302609i	0.994544	−	0.104320i	$-0.0332665\pi$
$743$	2.21018	+	8.24852i	0.0810838	+	0.302609i	−0.913460	+	0.406928i	$0.866600\pi$
$744$	−13.9014	−	10.2392i	−0.509650	−	0.375388i
$745$		0			0
$746$			35.7776i			1.30991i
$747$	0.810797	−	1.54122i	0.0296655	−	0.0563903i
$748$	0.764383	+	0.764383i	0.0279486	+	0.0279486i
$749$	−5.18310	−	8.97739i	−0.189386	−	0.328027i
$750$		0			0
$751$	2.32268	−	4.02301i	0.0847560	−	0.146802i	−0.820531	−	0.571602i	$-0.806322\pi$
$751$	2.32268	−	4.02301i	0.0847560	−	0.146802i	0.905287	+	0.424800i	$0.139656\pi$
$752$	−18.8900	+	5.06156i	−0.688848	+	0.184576i
$753$	22.4828	+	28.1374i	0.819319	+	1.02538i
$754$	−5.97796	+	3.45138i	−0.217704	+	0.125692i
$755$		0			0
$756$	2.34035	−	6.75030i	0.0851175	−	0.245506i
$757$	3.09830	−	3.09830i	0.112609	−	0.112609i	−0.648557	−	0.761166i	$-0.724627\pi$
$757$	3.09830	−	3.09830i	0.112609	−	0.112609i	0.761166	+	0.648557i	$0.224627\pi$
$758$	−17.9252	−	4.80304i	−0.651072	−	0.174454i
$759$	13.9182	+	1.55474i	0.505199	+	0.0564337i
$760$		0			0
$761$	38.9876	+	22.5095i	1.41330	+	0.815968i	0.995698	−	0.0926625i	$-0.0295377\pi$
$761$	38.9876	+	22.5095i	1.41330	+	0.815968i	0.417601	+	0.908631i	$0.362871\pi$
$762$	43.9505	+	17.2009i	1.59216	+	0.623122i
$763$	−0.515595	+	1.92422i	−0.0186658	+	0.0696616i
$764$	17.7890			0.643584
$765$		0			0
$766$	−25.2991			−0.914094
$767$	0.191415	−	0.714369i	0.00691158	−	0.0257944i
$768$	−4.15834	−	27.4111i	−0.150051	−	0.989114i
$769$	5.40503	+	3.12060i	0.194910	+	0.112532i	0.594279	−	0.804259i	$-0.297437\pi$
$769$	5.40503	+	3.12060i	0.194910	+	0.112532i	−0.399369	+	0.916790i	$0.630771\pi$
$770$		0			0
$771$	10.7951	−	14.6561i	0.388777	−	0.527828i
$772$	−15.3095	−	4.10216i	−0.551000	−	0.147640i
$773$	−19.5366	+	19.5366i	−0.702681	+	0.702681i	−0.964985	−	0.262304i	$-0.915518\pi$
$773$	−19.5366	+	19.5366i	−0.702681	+	0.702681i	0.262304	+	0.964985i	$0.415518\pi$
$774$	−14.4051	+	15.5846i	−0.517781	+	0.560178i
$775$		0			0
$776$	−9.47158	+	5.46842i	−0.340010	+	0.196305i
$777$	8.91613	−	22.7819i	0.319864	−	0.817296i
$778$	−40.9192	+	10.9643i	−1.46702	+	0.393088i
$779$	−4.65823	+	8.06829i	−0.166898	+	0.289076i
$780$		0			0
$781$	14.4691	+	25.0613i	0.517747	+	0.896764i
$782$	1.03156	+	1.03156i	0.0368887	+	0.0368887i
$783$	9.14265	−	13.4927i	0.326732	−	0.482190i
$784$			18.6129i			0.664748i
$785$		0			0
$786$	−1.60363	+	14.3558i	−0.0571995	+	0.512054i
$787$	−7.59393	−	28.3409i	−0.270694	−	1.01024i	−0.958672	−	0.284513i	$-0.908168\pi$
$787$	−7.59393	−	28.3409i	−0.270694	−	1.01024i	0.687978	−	0.725732i	$-0.258499\pi$
$788$	1.82590	+	6.81437i	0.0650451	+	0.242752i
$789$	23.7070	−	10.3702i	0.843992	−	0.369190i
$790$		0			0
$791$		−	15.0109i		−	0.533725i
$792$	−19.6906	−	10.3587i	−0.699676	−	0.368082i
$793$	−5.54513	−	5.54513i	−0.196913	−	0.196913i
$794$	−7.01613	−	12.1523i	−0.248993	−	0.431269i
$795$		0			0
$796$	−1.54321	+	2.67291i	−0.0546975	+	0.0947388i
$797$	−1.69461	+	0.454070i	−0.0600263	+	0.0160840i	−0.288707	−	0.957417i	$-0.593225\pi$
$797$	−1.69461	+	0.454070i	−0.0600263	+	0.0160840i	0.228681	+	0.973501i	$0.426559\pi$
$798$	−32.0234	+	4.85803i	−1.13362	+	0.171972i
$799$	−1.34185	+	0.774718i	−0.0474712	+	0.0274075i
$800$		0			0
$801$	−10.8791	+	48.0876i	−0.384394	+	1.69909i
$802$	32.1473	−	32.1473i	1.13516	−	1.13516i
$803$	6.37700	+	1.70871i	0.225039	+	0.0602991i
$804$	5.95185	+	13.6063i	0.209905	+	0.479858i
$805$		0			0
$806$	9.24736	+	5.33897i	0.325724	+	0.188057i
$807$	1.05815	−	0.845499i	0.0372486	−	0.0297630i
$808$	−2.90414	+	10.8384i	−0.102167	+	0.381294i
$809$	−27.5870			−0.969908			−0.484954	−	0.874540i	$-0.661164\pi$
$809$	−27.5870			−0.969908			−0.484954	+	0.874540i	$0.661164\pi$
$810$		0			0
$811$	−44.5699			−1.56506			−0.782530	−	0.622613i	$-0.786071\pi$
$811$	−44.5699			−1.56506			−0.782530	+	0.622613i	$0.786071\pi$
$812$	−1.11622	+	4.16580i	−0.0391718	+	0.146191i
$813$	16.8705	−	13.4802i	0.591675	−	0.472770i
$814$	40.8165	+	23.5654i	1.43062	+	0.825968i
$815$		0			0
$816$	−1.34456	−	3.07375i	−0.0470690	−	0.107603i
$817$	25.6972	+	6.88556i	0.899033	+	0.240895i
$818$	−31.9621	+	31.9621i	−1.11753	+	1.11753i
$819$	1.57608	−	6.96656i	0.0550726	−	0.243431i
$820$		0			0
$821$	38.4678	−	22.2094i	1.34254	−	0.775114i	0.355357	−	0.934731i	$-0.384359\pi$
$821$	38.4678	−	22.2094i	1.34254	−	0.775114i	0.987179	+	0.159617i	$0.0510259\pi$
$822$	1.29943	−	0.197127i	0.0453228	−	0.00687559i
$823$	30.5686	−	8.19082i	1.06555	−	0.285514i	0.316888	−	0.948463i	$-0.397362\pi$
$823$	30.5686	−	8.19082i	1.06555	−	0.285514i	0.748665	+	0.662949i	$0.230695\pi$
$824$	−5.35341	+	9.27239i	−0.186495	+	0.323019i
$825$		0			0
$826$	−0.835543	−	1.44720i	−0.0290723	−	0.0503546i
$827$	−2.06846	−	2.06846i	−0.0719275	−	0.0719275i	0.670228	−	0.742155i	$-0.266196\pi$
$827$	−2.06846	−	2.06846i	−0.0719275	−	0.0719275i	−0.742155	+	0.670228i	$0.766196\pi$
$828$	4.54553	+	2.39129i	0.157968	+	0.0831030i
$829$			12.9618i			0.450182i	0.974338	+	0.225091i	$0.0722680\pi$
$829$			12.9618i			0.450182i	−0.974338	+	0.225091i	$0.927732\pi$
$830$		0			0
$831$	14.9062	−	6.52044i	0.517089	−	0.226192i
$832$	−1.04552	−	3.90193i	−0.0362469	−	0.135275i
$833$	0.381677	+	1.42444i	0.0132243	+	0.0493539i
$834$	−5.12614	+	45.8897i	−0.177504	+	1.58903i
$835$		0			0
$836$		−	17.2540i		−	0.596742i
$837$	−25.1471	−	1.81207i	−0.869210	−	0.0626344i
$838$	36.9202	+	36.9202i	1.27539	+	1.27539i
$839$	−9.19525	−	15.9266i	−0.317455	−	0.549849i	0.662501	−	0.749061i	$-0.269495\pi$
$839$	−9.19525	−	15.9266i	−0.317455	−	0.549849i	−0.979956	+	0.199212i	$0.936162\pi$
$840$		0			0
$841$	9.58072	−	16.5943i	0.330370	−	0.572217i
$842$	−49.5699	+	13.2822i	−1.70829	+	0.457736i
$843$	−19.3906	+	49.5456i	−0.667848	+	1.70644i
$844$	−0.864691	+	0.499230i	−0.0297639	+	0.0171842i
$845$		0			0
$846$	−13.3909	+	14.4874i	−0.460390	+	0.498087i
$847$	2.58483	−	2.58483i	0.0888158	−	0.0888158i
$848$	50.5371	+	13.5414i	1.73545	+	0.465013i
$849$	19.3214	−	26.2320i	0.663109	−	0.900279i
$850$		0			0
$851$	15.2312	+	8.79374i	0.522119	+	0.301445i
$852$	1.59180	+	10.4929i	0.0545341	+	0.359480i
$853$	−3.57544	+	13.3437i	−0.122421	+	0.456880i	−0.999735	−	0.0230366i	$-0.992667\pi$
$853$	−3.57544	+	13.3437i	−0.122421	+	0.456880i	0.877314	+	0.479917i	$0.159333\pi$
$854$	−17.7193			−0.606342
$855$		0			0
$856$	−11.8392			−0.404657
$857$	−1.57903	+	5.89302i	−0.0539387	+	0.201302i	−0.987637	−	0.156759i	$-0.949895\pi$
$857$	−1.57903	+	5.89302i	−0.0539387	+	0.201302i	0.933698	+	0.358061i	$0.116562\pi$
$858$	12.8139	+	5.01495i	0.437458	+	0.171208i
$859$	16.1515	+	9.32505i	0.551081	+	0.318166i	0.749558	−	0.661939i	$-0.230266\pi$
$859$	16.1515	+	9.32505i	0.551081	+	0.318166i	−0.198477	+	0.980106i	$0.563600\pi$
$860$		0			0
$861$	−4.61347	−	0.515351i	−0.157226	−	0.0175631i
$862$	−52.4948	−	14.0659i	−1.78798	−	0.479088i
$863$	9.43441	−	9.43441i	0.321151	−	0.321151i	−0.528058	−	0.849209i	$-0.677079\pi$
$863$	9.43441	−	9.43441i	0.321151	−	0.321151i	0.849209	+	0.528058i	$0.177079\pi$
$864$	−13.9839	−	16.1558i	−0.475744	−	0.549631i
$865$		0			0
$866$	14.7822	−	8.53448i	0.502318	−	0.290013i
$867$	18.2146	+	22.7957i	0.618601	+	0.774183i
$868$	6.44412	−	1.72670i	0.218728	−	0.0586079i
$869$	14.5254	−	25.1588i	0.492742	−	0.853454i
$870$		0			0
$871$	7.42362	+	12.8581i	0.251540	+	0.435680i
$872$	1.60880	+	1.60880i	0.0544808	+	0.0544808i
$873$	−7.43573	+	14.1344i	−0.251661	+	0.478376i
$874$		−	23.2849i		−	0.787625i
$875$		0			0
$876$	1.94948	+	1.43591i	0.0658670	+	0.0485149i
$877$	12.7214	+	47.4768i	0.429570	+	1.60318i	0.753736	+	0.657177i	$0.228250\pi$
$877$	12.7214	+	47.4768i	0.429570	+	1.60318i	−0.324166	+	0.946000i	$0.605084\pi$
$878$	−9.67374	−	36.1029i	−0.326473	−	1.21841i
$879$	−47.1375	−	34.7195i	−1.58991	−	1.17106i
$880$		0			0
$881$		−	17.7562i		−	0.598222i	−0.954218	−	0.299111i	$-0.903310\pi$
$881$		−	17.7562i		−	0.598222i	0.954218	−	0.299111i	$-0.0966901\pi$
$882$	10.0200	+	15.8794i	0.337392	+	0.534687i
$883$	−8.09196	−	8.09196i	−0.272316	−	0.272316i	0.557716	−	0.830032i	$-0.311678\pi$
$883$	−8.09196	−	8.09196i	−0.272316	−	0.272316i	−0.830032	+	0.557716i	$0.811678\pi$
$884$	0.198173	+	0.343246i	0.00666528	+	0.0115446i
$885$		0			0
$886$	6.42494	−	11.1283i	0.215850	−	0.373863i
$887$	−10.2623	+	2.74978i	−0.344575	+	0.0923287i	−0.426956	−	0.904272i	$-0.640414\pi$
$887$	−10.2623	+	2.74978i	−0.344575	+	0.0923287i	0.0823810	+	0.996601i	$0.473748\pi$
$888$	−17.4417	−	21.8284i	−0.585306	−	0.732515i
$889$	25.5305	−	14.7401i	0.856267	−	0.494366i
$890$		0			0
$891$	−32.3898	+	2.55174i	−1.08510	+	0.0854867i
$892$	−4.48293	+	4.48293i	−0.150100	+	0.150100i
$893$	23.8881	+	6.40079i	0.799383	+	0.214194i
$894$	19.6992	+	2.20051i	0.658839	+	0.0735962i
$895$		0			0
$896$	−20.7164	−	11.9606i	−0.692087	−	0.399577i
$897$	4.78165	+	1.87139i	0.159655	+	0.0624840i
$898$	16.4169	−	61.2688i	0.547840	−	2.04457i
$899$	15.2193			0.507594
$900$		0			0
$901$	4.14526			0.138098
$902$	2.31465	−	8.63839i	0.0770694	−	0.287627i
$903$	1.98822	+	13.1060i	0.0661639	+	0.436142i
$904$	−14.8471	−	8.57197i	−0.493807	−	0.285099i
$905$		0			0
$906$	−14.7097	+	19.9708i	−0.488696	+	0.663485i
$907$	−7.49600	−	2.00855i	−0.248901	−	0.0666927i	0.132212	−	0.991222i	$-0.457792\pi$
$907$	−7.49600	−	2.00855i	−0.248901	−	0.0666927i	−0.381112	+	0.924529i	$0.624459\pi$
$908$	4.98428	−	4.98428i	0.165409	−	0.165409i
$909$	4.85961	+	15.6483i	0.161183	+	0.519021i
$910$		0			0
$911$	−11.1341	+	6.42830i	−0.368890	+	0.212979i	−0.672974	−	0.739667i	$-0.734983\pi$
$911$	−11.1341	+	6.42830i	−0.368890	+	0.212979i	0.304083	+	0.952645i	$0.401650\pi$
$912$	−19.5160	+	49.8660i	−0.646240	+	1.65123i
$913$	2.02419	−	0.542379i	0.0669908	−	0.0179501i
$914$	23.1537	−	40.1034i	0.765857	−	1.32650i
$915$		0			0
$916$	−7.59207	−	13.1498i	−0.250849	−	0.434483i
$917$	6.38005	+	6.38005i	0.210688	+	0.210688i
$918$	−2.80181	−	1.89850i	−0.0924734	−	0.0626600i
$919$			30.7848i			1.01550i	0.861505	+	0.507749i	$0.169522\pi$
$919$			30.7848i			1.01550i	−0.861505	+	0.507749i	$0.830478\pi$
$920$		0			0
$921$	−0.616543	+	5.51934i	−0.0203158	+	0.181869i
$922$	10.5491	+	39.3699i	0.347417	+	1.29658i
$923$	2.74611	+	10.2486i	0.0903893	+	0.337337i
$924$	7.87662	−	3.44549i	0.259122	−	0.113348i
$925$		0			0
$926$			29.7259i			0.976854i
$927$	0.614455	+	15.6230i	0.0201814	+	0.513125i
$928$	9.12048	+	9.12048i	0.299394	+	0.299394i
$929$	12.1446	+	21.0351i	0.398453	+	0.690141i	0.993535	−	0.113524i	$-0.0362139\pi$
$929$	12.1446	+	21.0351i	0.398453	+	0.690141i	−0.595082	+	0.803665i	$0.702881\pi$
$930$		0			0
$931$	11.7688	−	20.3842i	0.385708	−	0.668066i
$932$	5.69388	−	1.52567i	0.186509	−	0.0499750i
$933$	3.69155	−	0.560018i	0.120856	−	0.0183342i
$934$	−45.3882	+	26.2049i	−1.48515	+	0.857451i
$935$		0			0
$936$	−5.99052	−	5.53714i	−0.195806	−	0.180987i
$937$	18.4403	−	18.4403i	0.602420	−	0.602420i	−0.338534	−	0.940954i	$-0.609931\pi$
$937$	18.4403	−	18.4403i	0.602420	−	0.602420i	0.940954	+	0.338534i	$0.109931\pi$
$938$	32.4048	+	8.68284i	1.05805	+	0.283505i
$939$	15.0845	+	34.4842i	0.492265	+	1.12535i
$940$		0			0
$941$	−34.2802	−	19.7917i	−1.11750	−	0.645191i	−0.176741	−	0.984257i	$-0.556556\pi$
$941$	−34.2802	−	19.7917i	−1.11750	−	0.645191i	−0.940763	+	0.339066i	$0.889889\pi$
$942$	3.74829	−	2.99503i	0.122126	−	0.0975832i
$943$	0.863741	−	3.22353i	0.0281273	−	0.104972i
$944$	−2.76275			−0.0899200
$945$		0			0
$946$	−25.5377			−0.830301
$947$	10.7139	−	39.9850i	0.348156	−	1.29934i	−0.540725	−	0.841199i	$-0.681850\pi$
$947$	10.7139	−	39.9850i	0.348156	−	1.29934i	0.888881	−	0.458138i	$-0.151483\pi$
$948$	8.32346	−	6.65076i	0.270334	−	0.216006i
$949$	2.09629	+	1.21029i	0.0680485	+	0.0392878i
$950$		0			0
$951$	−3.21843	−	7.35754i	−0.104365	−	0.238585i
$952$	−1.39834	−	0.374683i	−0.0453203	−	0.0121435i
$953$	17.2048	−	17.2048i	0.557319	−	0.557319i	−0.371224	−	0.928543i	$-0.621062\pi$
$953$	17.2048	−	17.2048i	0.557319	−	0.557319i	0.928543	+	0.371224i	$0.121062\pi$
$954$	50.4049	−	15.6534i	1.63192	−	0.506796i
$955$		0			0
$956$	4.60979	−	2.66147i	0.149091	−	0.0860780i
$957$	19.3907	−	2.94163i	0.626814	−	0.0950893i
$958$	−21.7218	+	5.82033i	−0.701798	+	0.188046i
$959$	0.410471	−	0.710957i	0.0132548	−	0.0229580i
$960$		0			0
$961$	3.72853	+	6.45800i	0.120275	+	0.208323i
$962$	12.2191	+	12.2191i	0.393959	+	0.393959i
$963$	−14.6212	+	9.22608i	−0.471160	+	0.297306i
$964$			17.9875i			0.579339i
$965$		0			0
$966$	10.6298	−	4.64983i	0.342008	−	0.149606i
$967$	−5.71932	−	21.3448i	−0.183921	−	0.686402i	−0.994859	−	0.101270i	$-0.967709\pi$
$967$	−5.71932	−	21.3448i	−0.183921	−	0.686402i	0.810938	−	0.585132i	$-0.198957\pi$
$968$	−1.08056	−	4.03269i	−0.0347304	−	0.129616i
$969$	−0.470998	+	4.21642i	−0.0151306	+	0.135451i
$970$		0			0
$971$			3.58038i			0.114900i	0.998348	+	0.0574499i	$0.0182969\pi$
$971$			3.58038i			0.114900i	−0.998348	+	0.0574499i	$0.981703\pi$
$972$	−11.4028	−	3.45776i	−0.365746	−	0.110908i
$973$	20.3944	+	20.3944i	0.653815	+	0.653815i
$974$	20.9139	+	36.2239i	0.670124	+	1.16069i
$975$		0			0
$976$	−14.6474	+	25.3700i	−0.468851	+	0.812074i
$977$	19.8966	−	5.33127i	0.636548	−	0.170562i	0.0739084	−	0.997265i	$-0.476453\pi$
$977$	19.8966	−	5.33127i	0.636548	−	0.170562i	0.562639	+	0.826703i	$0.309786\pi$
$978$	−15.6027	+	39.8670i	−0.498920	+	1.27481i
$979$	−51.3796	+	29.6640i	−1.64210	+	0.948067i
$980$		0			0
$981$	3.24053	+	0.733120i	0.103462	+	0.0234067i
$982$	−24.4066	+	24.4066i	−0.778846	+	0.778846i
$983$	−28.2934	−	7.58120i	−0.902420	−	0.241803i	−0.222365	−	0.974963i	$-0.571378\pi$
$983$	−28.2934	−	7.58120i	−0.902420	−	0.241803i	−0.680055	+	0.733161i	$0.738044\pi$
$984$	−3.14425	+	4.26883i	−0.100235	+	0.136085i
$985$		0			0
$986$	1.76930	+	1.02151i	0.0563460	+	0.0325314i
$987$	1.84824	+	12.1833i	0.0588302	+	0.387800i
$988$	1.63732	−	6.11057i	0.0520902	−	0.194403i
$989$	−9.52971			−0.303027
$990$		0			0
$991$	−21.0816			−0.669679			−0.334840	−	0.942275i	$-0.608682\pi$
$991$	−21.0816			−0.669679			−0.334840	+	0.942275i	$0.608682\pi$
$992$	5.16409	−	19.2726i	0.163960	−	0.611907i
$993$	−46.9518	−	18.3755i	−1.48997	−	0.583128i
$994$	20.7621	+	11.9870i	0.658535	+	0.380205i
$995$		0			0
$996$	0.763794	+	0.0853203i	0.0242017	+	0.00270348i
$997$	−49.9569	−	13.3859i	−1.58215	−	0.423936i	−0.642559	−	0.766236i	$-0.722127\pi$
$997$	−49.9569	−	13.3859i	−1.58215	−	0.423936i	−0.939591	+	0.342300i	$0.888794\pi$
$998$	11.6227	−	11.6227i	0.367909	−	0.367909i
$999$	−38.5506	−	13.3656i	−1.21969	−	0.422868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.p.b.68.3		16
3.2	odd	2		675.2.q.a.368.2		16
5.2	odd	4	inner	225.2.p.b.32.3		16
5.3	odd	4		45.2.l.a.32.2	yes	16
5.4	even	2		45.2.l.a.23.2	yes	16
9.2	odd	6	inner	225.2.p.b.218.3		16
9.7	even	3		675.2.q.a.143.2		16
15.2	even	4		675.2.q.a.557.2		16
15.8	even	4		135.2.m.a.17.3		16
15.14	odd	2		135.2.m.a.98.3		16
20.3	even	4		720.2.cu.c.257.3		16
20.19	odd	2		720.2.cu.c.113.1		16
45.2	even	12	inner	225.2.p.b.182.3		16
45.4	even	6		405.2.f.a.323.2		16
45.7	odd	12		675.2.q.a.332.2		16
45.13	odd	12		405.2.f.a.242.7		16
45.14	odd	6		405.2.f.a.323.7		16
45.23	even	12		405.2.f.a.242.2		16
45.29	odd	6		45.2.l.a.38.2	yes	16
45.34	even	6		135.2.m.a.8.3		16
45.38	even	12		45.2.l.a.2.2	✓	16
45.43	odd	12		135.2.m.a.62.3		16
180.83	odd	12		720.2.cu.c.497.1		16
180.119	even	6		720.2.cu.c.353.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.2	✓	16	45.38	even	12
45.2.l.a.23.2	yes	16	5.4	even	2
45.2.l.a.32.2	yes	16	5.3	odd	4
45.2.l.a.38.2	yes	16	45.29	odd	6
135.2.m.a.8.3		16	45.34	even	6
135.2.m.a.17.3		16	15.8	even	4
135.2.m.a.62.3		16	45.43	odd	12
135.2.m.a.98.3		16	15.14	odd	2
225.2.p.b.32.3		16	5.2	odd	4	inner
225.2.p.b.68.3		16	1.1	even	1	trivial
225.2.p.b.182.3		16	45.2	even	12	inner
225.2.p.b.218.3		16	9.2	odd	6	inner
405.2.f.a.242.2		16	45.23	even	12
405.2.f.a.242.7		16	45.13	odd	12
405.2.f.a.323.2		16	45.4	even	6
405.2.f.a.323.7		16	45.14	odd	6
675.2.q.a.143.2		16	9.7	even	3
675.2.q.a.332.2		16	45.7	odd	12
675.2.q.a.368.2		16	3.2	odd	2
675.2.q.a.557.2		16	15.2	even	4
720.2.cu.c.113.1		16	20.19	odd	2
720.2.cu.c.257.3		16	20.3	even	4
720.2.cu.c.353.3		16	180.119	even	6
720.2.cu.c.497.1		16	180.83	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.430324 - 1.60599i) q^{2} +(-1.35314 + 1.08121i) q^{3} +(-0.661975 - 0.382191i) q^{4} +(1.15412 + 2.63840i) q^{6} +(1.73749 + 0.465559i) q^{7} +(1.45267 - 1.45267i) q^{8} +(0.661975 - 2.92605i) q^{9} +O(q^{10})\)	\(q+(0.430324 - 1.60599i) q^{2} +(-1.35314 + 1.08121i) q^{3} +(-0.661975 - 0.382191i) q^{4} +(1.15412 + 2.63840i) q^{6} +(1.73749 + 0.465559i) q^{7} +(1.45267 - 1.45267i) q^{8} +(0.661975 - 2.92605i) q^{9} +(3.12636 - 1.80501i) q^{11} +(1.30897 - 0.198575i) q^{12} +(1.27850 - 0.342574i) q^{13} +(1.49537 - 2.59005i) q^{14} +(-2.47224 - 4.28205i) q^{16} +(-0.277007 - 0.277007i) q^{17} +(-4.41435 - 2.32228i) q^{18} +6.25273i q^{19} +(-2.85443 + 1.24862i) q^{21} +(-1.55348 - 5.79765i) q^{22} +(-0.579699 - 2.16347i) q^{23} +(-0.395027 + 3.53631i) q^{24} -2.20068i q^{26} +(2.26793 + 4.67509i) q^{27} +(-0.972242 - 0.972242i) q^{28} +(-1.56832 - 2.71642i) q^{29} +(-2.42605 + 4.20205i) q^{31} +(-3.97202 + 1.06430i) q^{32} +(-2.27882 + 5.82268i) q^{33} +(-0.564074 + 0.325668i) q^{34} +(-1.55652 + 1.68397i) q^{36} +(-5.55242 + 5.55242i) q^{37} +(10.0418 + 2.69070i) q^{38} +(-1.35960 + 1.84588i) q^{39} +(1.29036 + 0.744991i) q^{41} +(0.776946 + 5.12150i) q^{42} +(1.10121 - 4.10976i) q^{43} -2.75943 q^{44} -3.72396 q^{46} +(1.02368 - 3.82042i) q^{47} +(7.97508 + 3.12120i) q^{48} +(-3.26005 - 1.88219i) q^{49} +(0.674332 + 0.0753268i) q^{51} +(-0.977265 - 0.261857i) q^{52} +(-7.48222 + 7.48222i) q^{53} +(8.48410 - 1.63047i) q^{54} +(3.20031 - 1.84770i) q^{56} +(-6.76051 - 8.46082i) q^{57} +(-5.03742 + 1.34977i) q^{58} +(0.279377 - 0.483896i) q^{59} +(-2.96237 - 5.13097i) q^{61} +(5.70446 + 5.70446i) q^{62} +(2.51243 - 4.77580i) q^{63} -3.05196i q^{64} +(8.37054 + 6.16540i) q^{66} +(2.90325 + 10.8351i) q^{67} +(0.0775020 + 0.289242i) q^{68} +(3.12357 + 2.30070i) q^{69} +8.01611i q^{71} +(-3.28897 - 5.21223i) q^{72} +(1.29315 + 1.29315i) q^{73} +(6.52779 + 11.3065i) q^{74} +(2.38974 - 4.13915i) q^{76} +(6.27237 - 1.68068i) q^{77} +(2.37939 + 2.97783i) q^{78} +(6.96917 - 4.02365i) q^{79} +(-8.12358 - 3.87395i) q^{81} +(1.75172 - 1.75172i) q^{82} +(0.560714 + 0.150243i) q^{83} +(2.36678 + 0.264383i) q^{84} +(-6.12636 - 3.53706i) q^{86} +(5.05917 + 1.98001i) q^{87} +(1.91950 - 7.16367i) q^{88} -16.4343 q^{89} +2.38087 q^{91} +(-0.443112 + 1.65372i) q^{92} +(-1.26050 - 8.30903i) q^{93} +(-5.69504 - 3.28804i) q^{94} +(4.22396 - 5.73472i) q^{96} +(-5.14224 - 1.37786i) q^{97} +(-4.42566 + 4.42566i) q^{98} +(-3.21197 - 10.3428i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7}+O(q^{10}) \) 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7	\( 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7} + 6 q^{12} + 2 q^{13} - 8 q^{16} - 36 q^{18} - 12 q^{21} + 10 q^{22} - 18 q^{23} - 18 q^{27} + 16 q^{28} - 4 q^{31} - 30 q^{32} + 12 q^{33} - 48 q^{36} - 4 q^{37} + 30 q^{38} - 24 q^{41} - 6 q^{42} + 2 q^{43} + 32 q^{46} + 12 q^{47} + 30 q^{48} + 36 q^{51} + 14 q^{52} + 36 q^{56} + 6 q^{57} + 6 q^{58} + 8 q^{61} - 36 q^{63} + 36 q^{66} - 4 q^{67} - 42 q^{68} - 18 q^{72} + 8 q^{73} + 24 q^{76} + 6 q^{77} + 42 q^{78} - 48 q^{81} - 32 q^{82} + 66 q^{83} - 48 q^{86} + 18 q^{87} - 18 q^{88} - 40 q^{91} + 60 q^{92} + 18 q^{93} - 24 q^{96} - 28 q^{97}+O(q^{100}) \) 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7 + 6 * q^12 + 2 * q^13 - 8 * q^16 - 36 * q^18 - 12 * q^21 + 10 * q^22 - 18 * q^23 - 18 * q^27 + 16 * q^28 - 4 * q^31 - 30 * q^32 + 12 * q^33 - 48 * q^36 - 4 * q^37 + 30 * q^38 - 24 * q^41 - 6 * q^42 + 2 * q^43 + 32 * q^46 + 12 * q^47 + 30 * q^48 + 36 * q^51 + 14 * q^52 + 36 * q^56 + 6 * q^57 + 6 * q^58 + 8 * q^61 - 36 * q^63 + 36 * q^66 - 4 * q^67 - 42 * q^68 - 18 * q^72 + 8 * q^73 + 24 * q^76 + 6 * q^77 + 42 * q^78 - 48 * q^81 - 32 * q^82 + 66 * q^83 - 48 * q^86 + 18 * q^87 - 18 * q^88 - 40 * q^91 + 60 * q^92 + 18 * q^93 - 24 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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